text: hereinafter , embodiments of the present invention will be described in detail with reference to the accompanying drawings . in describing the present invention below , terms indicating components of the present invention are named in consideration of functions thereof . therefore , the terms should not be understood as limiting technical components of the present invention . for reference , it is to be noted that , in the present specification , the term “ front ” refers to a direction toward an object from a lens module , while the term “ rear ” refers to a direction toward an image sensor from a lens module . in addition , it is to be noted that , in each lens , a first surface refers to a surface toward an object and a second surface refers to a surface adjacent to an image . fig1 is a structural view of a lens module according to a first embodiment of the present invention ; fig2 a , 2 b , and 2 c are graphs showing aberration characteristics of the lens module of fig1 ; fig3 is a structural view of a lens module according to a second embodiment of the present invention ; fig4 a , 4 b , and 4 c are graphs showing aberration characteristics of the lens module of fig3 ; fig5 is a structural view of a lens module according to a third embodiment of the present invention ; fig6 a , 6 b , and 6 c are graphs showing aberration characteristics of the lens module of fig5 ; fig7 is a structural view of a lens module according to a fourth embodiment of the present invention ; fig8 a , 8 b , and 8 c are graphs showing aberration characteristics of the lens module of fig7 ; fig9 is a structural view of a lens module according to a fifth embodiment of the present invention ; and fig1 a , 10 b , and 10 c are graphs showing aberration characteristics of the lens module of fig9 . a lens module 100 according to the present invention may include a first lens 10 , a second lens 20 , a third lens 30 , a fourth lens 40 , and a fifth lens 50 , and may selectively further include an aperture and a filter member 60 , and an image sensor 70 . the first lens 10 to the fifth lens 50 may be sequentially disposed from an object ( that is , a subject or an object to be photographed ) toward an image ( that is , the image sensor ). the first lens 10 , the second lens 20 , the third lens 30 , the fourth lens 40 , and the fifth lens 50 may be all formed of plastic . as such , when all the lenses 10 , 20 , 30 , 40 and 50 are formed of plastic , the manufacturing cost of the lens module 100 may be reduced and the lens modules 100 may be conveniently mass - produced . in addition , when the lenses 10 , 20 , 30 , 40 , and 50 are formed of plastic , first and second surfaces s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , and s10 of the lenses are easily processed , and thus , the surfaces of the lenses may be formed to have a spherical or aspherical shape . in the lens module 100 , the first lens 10 may be disposed closest to the object . the first lens 10 may have positive refractive power overall . in addition , the first surface s1 of the first lens 10 may be convex toward the object , and the second surface s2 thereof may be convex toward the image . in detail , the first surface s1 may be more convex than the second surface s2 . at least one of the first surface s1 and the second surface s2 of the first lens 10 may be aspherical . however , as needed , both of the first surface s1 and the second surface s2 of the first lens 10 may be aspherical . the second lens 20 may be disposed in the rear of the first lens 10 ( that is , in the direction toward the image ). the second lens 20 may have negative refractive power overall , and may be formed of plastic in like manner to the first lens 10 . the first surface s3 of the second lens 20 may be convex toward the object , and the second surface s4 thereof may be concave toward the object . in addition , the second lens 20 may have at least one aspherical surface . for example , at least one of the first surface s3 and the second surface s4 of the second lens 20 may be aspherical . however , as needed , both of the first surface s3 and the second surface s4 of the second lens 20 may be aspherical . the second lens 20 may have an abbe number satisfying mathematical expression 1 below . as such , when the abbe number of the second lens 20 is below 40 , chromatic aberration caused by the first lens 10 may be effectively corrected . when the abbe number of the second lens 20 is above 40 , a difference between an abbe number of the first lens 10 and the abbe number of the second lens 20 may be reduced ( in general , the abbe number of the first lens 10 is between 50 and 60 ), such that a chromatic aberration correction effect through the second lens 20 may be deteriorated . therefore , the second lens 20 may be manufactured in such a manner that the abbe number thereof is below 40 , as supposed in mathematical expression 1 . the abbe number of the second lens 20 may be 20 to 30 . the third lens 30 may be disposed in the rear of the second lens 20 . the third lens 30 may have positive refractive power overall , and may be formed of plastic . however , as needed , the third lens 30 may have negative refractive power . the first surface s5 of the third lens 30 may be concave , and the second surface s6 thereof may be convex toward the image . here , in some cases , the first surface s5 of the third lens 30 may be convex toward the object ( please refer to the third embodiment of the present invention shown in fig5 ). meanwhile , the second lens 20 and the third lens 30 as described above may satisfy mathematical expression 2 . here , f2 is a focal distance of the second lens 20 and f3 is a focal distance of the third lens 30 . in the lens module , if a value of f3 / f2 is below the lower limit according to mathematical expression 2 , the refractive power of the second lens may be increased , and thus , it may be difficult to manufacture the second lens . in the same manner , in the lens module , if the value of f3 / f2 is above the upper limit according to mathematical expression 2 , the refractive power of the third lens may be increased , and thus , it may be difficult to manufacture the third lens . therefore , it is desirable to satisfy conditions for mathematical expression 2 to allow for mass - production of the lens module . the fourth lens 40 may be disposed in the rear of the third lens 30 . the fourth lens 40 may have negative refractive power , and may be formed of plastic . the first surface s7 of the fourth lens 40 may be concave , and the second surface s8 thereof may be convex toward the image . in addition , the fourth lens 40 may have a meniscus shape , convex toward the image , overall . the fourth lens 40 may satisfy mathematical expressions 3 to 5 . here , ∪ 1 is the abbe number of the first lens , and ∪ 4 is an abbe number of the fourth lens . mathematical expression 3 may be a limitation condition with respect to chromatic aberration of the lens module . that is , when a lens module satisfying mathematical expression 3 is manufactured , the chromatic aberration correction effect may be improved through the first lens 10 and the fourth lens 40 . however , if a value of ∪ 1 -∪ 4 is below the lower limit according to mathematical expression 3 , a lens of glass needs to be used , and thus , unit costs for manufacturing the lens module 100 may be increased . unlike this , if the value of ∪ 1 -∪ 4 is above the upper limit according to mathematical expression 3 , the chromatic aberration correction effect may be deteriorated , and thus , it may be difficult to manufacture a lens module capable of realizing high resolution . here , f1 is a focal distance of the first lens , and f4 is a focal distance of the fourth lens . mathematical expression 4 may be a limitation condition for limiting the refractive power of the fourth lens 40 . that is , if a value of f4 / f1 is above the upper limit according to mathematical expression 4 , the refractive power of the fourth lens 40 in the lens module may be increased , and thus , resolution of the lens module 100 may be deteriorated or an overall length of the lens module 100 ( that is , an overall length of the optical system ) may be increased . here , f is an overall focal distance of the lens module , and f4 is the focal distance of the fourth lens . mathematical expression 5 may be a limitation condition for limiting the refractive power of the fourth lens 40 , like mathematical expression 4 . that is , if a value of f4 / f is above the upper limit according to mathematical expression 5 , the ( negative ) refractive power of the fourth lens 40 in the lens module may be increased , and thus , resolution of the lens module 100 may be deteriorated or the overall focal distance of the lens module may become excessively small , so that distortion correction may be difficult ( or a viewing angle of the lens module may be excessively large , and thus , a distortion phenomenon may occur ). therefore , mathematical expression 4 and mathematical expression 5 all may need to be satisfied in order to decrease the overall length of the lens module 100 . the fifth lens 50 may be disposed in the rear of the fourth lens 40 . the fifth lens 50 may have negative refractive power , and may be formed of plastic . the first surface s9 of the fifth lens 50 may be convex toward the object at an intersection thereof with an optical axis ( c - c ) and may be concave at a peripheral portion thereof based on the optical axis ( c - c ). in addition , the second surface s10 of the fifth lens 50 may be concave at an intersection thereof with the optical axis ( c - c ) and may be convex at a peripheral portion thereof based on the optical axis ( c - c ). that is , at least one inflection point may be formed on the first surface s9 and the second surface s10 of the fifth lens 50 . the filter member 60 may be disposed in the rear of the fifth lens 50 . both surfaces of the filter member 60 may flat planes , and may be formed of a material other than plastic . for example , the filter member 60 may be formed of glass . the filter member 60 may block infrared light . to achieve this , an ir blocking film may be attached to , or an ir blocking layer may be coated on , at least one surface of the filter member 60 . meanwhile , the filter member 60 may be omitted , depending on the type of the lens module 100 . the image sensor 70 may be disposed in the rear of the filter member 60 . the image sensor 70 may convert an image of the object , incident through the lenses 10 , 20 , 30 , 40 , and 50 into an electric signal . a charge - coupled device ( ccd ), complementary metal - oxide - semiconductor ( cmos ), or the like , may be used for the image sensor 70 , and the image sensor 70 may be manufactured in the form of chip scale package ( csp ). the aperture ( not shown ) may be disposed in front of the first lens 10 or between the first lens 10 and the second lens 20 . however , the aperture may be omitted as needed . the lens module 100 as described above may satisfy mathematical expression 6 . here , tl is an overall length of the optical system ( a length from the first surface s1 of the first lens to an upper surface of the image sensor 70 ), and f is the overall focal distance of the optical system . mathematical expression 6 may be a numerical value for limiting the viewing angle and the length of the lens module . that is , if a value of tl / f is below the lower limit according to mathematical expression 6 , it may be difficult to obtain the viewing angle of the lens module 100 . on the contrary , if the value of tl / f is above the upper limit according to mathematical expression 6 , the length ( that is , tl ) of the lens module 100 is extended , and thus , it is difficult to manufacture the lens module 100 so as to have a small size . meanwhile , at least one surface of the first lens 10 to the fourth lens 40 may be aspherical . aspherical coefficients of the lenses may be calculated by using mathematical expression 7 . here , c is curvature ( 1 / radius of curvature ), h is a radius from the center to a specific position in the lens , k is a conic coefficient , a is a 4 th - order coefficient , b is a 6 th - order coefficient , c is an 8 th - order coefficient , d is a 10 th - order coefficient , e is an 12 th - order coefficient , f is a 14 th - order coefficient , and z is sag at the specific position . for reference , k , a , b , c , d , e , and f values for respective embodiments are shown in tables 2 , 4 , 6 , 8 , and 10 . the lens module 100 as constructed above may realize high resolution through numerical limitations according to mathematical expressions 1 to 5 , and may be miniaturized . in addition , the lens module 100 may improve brightness of the lens module 100 by limiting the focal distance of the fourth lens 40 through mathematical expressions 4 and 5 . tables 1 to 10 below show numeral values in several embodiments of the lens module 100 having the above construction . the lens module 100 according to the first embodiment of the present invention will be described with reference to fig1 , 2 a , 2 b , and 2 c . the lens module 100 according to the first embodiment may include the first lens 10 having positive refractive power , the second lens 20 having negative refractive power , the third lens 30 having positive refractive power , the fourth lens 40 having negative refractive power , and the fifth lens 50 having negative refractive power . in the lens module 100 of the present embodiment , the focal distance f1 of the first lens 10 is 2 . 91 mm ; the focal distance f2 of the second lens 20 is − 5 . 68 mm ; the focal distance f3 of the third lens 30 is 8 . 44 mm ; the focal distance f4 of the fourth lens 40 is − 25 . 61 mm ; the focal distance f5 of the fifth lens 50 is − 12 . 01 mm ; the overall focal distance f is 4 . 12 mm ; and f number ( f no .) is 2 . 40 . meanwhile , tl according to the embodiment is 4 . 77 mm , the smallest among the accompanying embodiments , together with embodiment 2 . the lens module 100 according to the second embodiment may include the first lens 10 having positive refractive power , the second lens 20 having negative refractive power , the third lens 30 having positive refractive power , the fourth lens 40 having negative refractive power , and the fifth lens 50 having negative refractive power . in the lens module 100 of the present embodiment , the focal distance f1 of the first lens 10 is 2 . 86 mm ; the focal distance f2 of the second lens 20 is − 5 . 50 mm ; the focal distance f3 of the third lens 30 is 7 . 85 mm ; the focal distance f4 of the fourth lens 40 is − 100 . 00 mm ; the focal distance f5 of the fifth lens 50 is − 8 . 24 mm ; the overall focal distance f is 4 . 12 mm ; and f no . is 2 . 40 . in addition , tl according to the embodiment is 4 . 77 , the smallest , together with the first embodiment . the lens module 100 according to the third embodiment may include the first lens 10 having positive refractive power , the second lens 20 having negative refractive power , the third lens 30 having positive refractive power , the fourth lens 40 having negative refractive power , and the fifth lens 50 having negative refractive power . here , the first surface s5 of the third lens 30 may be convex toward the object , unlike the other embodiments . in addition , the fourth lens 40 may have an inflection point at a peripheral portion based on the optical axis ( c - c ) as shown in fig5 . in the lens module 100 of the present embodiment , the focal distance f1 of the first lens 10 is 3 . 23 mm ; the focal distance f2 of the second lens 20 is − 5 . 85 mm ; the focal distance f3 of the third lens 30 is 5 . 46 mm ; the focal distance f4 of the fourth lens 40 is − 100 . 00 mm ; the focal distance f5 of the fifth lens 50 is − 6 . 31 mm ; and the overall focal distance f is 4 . 16 mm . in addition , f no . of the present embodiment is 2 . 20 , brighter than the first and second embodiments . however , tl according to the embodiment is 4 . 87 , slightly larger than the first and second embodiments . the lens module 100 according to the fourth embodiment may include the first lens 10 having positive refractive power , the second lens 20 having negative refractive power , the third lens 30 having positive refractive power , the fourth lens 40 having negative refractive power , and the fifth lens 50 having negative refractive power . here , the fourth lens 40 may have an inflection point at the peripheral portion thereof based the optical axis ( c - c ) like in the third embodiment . in the lens module 100 of the present embodiment , the focal distance f1 of the first lens 10 is 3 . 52 mm ; the focal distance f2 of the second lens 20 is − 7 . 55 mm ; the focal distance f3 of the third lens 30 is 4 . 46 mm ; the focal distance f4 of the fourth lens 40 is − 95 . 01 mm ; the focal distance f5 of the fifth lens 50 is − 5 . 32 mm ; and the overall focal distance f is 4 . 21 mm . in addition , f no . and tl according to the embodiment are 2 . 20 and 4 . 87 , respectively . f no . of the present embodiment is low , similarly to the case of the third embodiment , but tl according to the embodiment is slightly larger as compared with those of the first and second embodiments . the lens module 100 according to the fifth embodiment may include the first lens 10 having positive refractive power , the second lens 20 having negative refractive power , the third lens 30 having positive refractive power , the fourth lens 40 having negative refractive power , and the fifth lens 50 having negative refractive power . in the lens module 100 of the present embodiment , the focal distance f1 of the first lens 10 is 3 . 09 mm ; the focal distance f2 of the second lens 20 is − 5 . 56 mm ; the focal distance f3 of the third lens 30 is 7 . 41 mm ; the focal distance f4 of the fourth lens 40 is − 91 . 69 mm ; the focal distance f5 of the fifth lens 50 is − 8 . 34 mm ; and the overall focal distance f is 4 . 25 mm . in addition , f no . of the present embodiment is 2 . 20 , brighter as compared with the first and second embodiments , but tl according to the embodiment is 5 . 05 , the greatest among the accompanying embodiments . here , the first and second embodiments may provide a relatively smaller tl than the other embodiments , while the third to fifth embodiments may provide a relatively brighter lens module than the other embodiments . while the present invention has been shown and described in connection with the embodiments , it will be apparent to those skilled in the art that modifications and variations can be made without departing from the spirit and scope of the invention as defined by the appended claims .