Consider the following premises. For all x_5, x_5 will write a letter if and only if x_5 will take a plane. For all x_5, x_5 will write a letter. There is at least one x_5 for which if x_5 were a doctor, then x_5 is taking a plane. Can we infer the following from them? There is at least one x_5 for which x_5 will take a plane.
 From the fact that for all x_5, x_5 will write a letter if and only if x_5 will take a plane we can infer that for all x_5, if x_5 writes a letter, then x_5 is taking a plane. From the fact that for all x_5, x_5 will write a letter we can infer that for all x_5, x_5 will write a letter or x_5 is a doctor. Finally, from the fact that for all x_5, if x_5 writes a letter, then x_5 is taking a plane, that there is at least one x_5 for which if x_5 were a doctor, then x_5 is taking a plane, and that for all x_5, x_5 will write a letter or x_5 is a doctor we can infer that there is at least one x_5 for which x_5 will take a plane. Therefore, the answer is yes.