5. Xiao Ming encountered a melon vendor on the street, hearing the vendor shout: “Large melons for 10 yuan each, medium melons for 10 yuan two, small melons for 10 yuan three. Pick and choose as you like.” Ming carefully examined the size and shape of the melons: the melons are nearly spherical, the diameter of the medium melon is approximately $\frac{3}{4}$ of the large melon's diameter, and the diameter of the small melon is approximately $\frac{4}{5}$ of the medium melon's diameter. After careful consideration, Xiao Ming spent 20 yuan to buy the option with the largest total volume ( ).
(A) two large melons
(B) four medium melons
(C) six small melons
(D) two medium melons and three small melons
5. A.

Let the radius of the large melon be $R$, and the volumes of the large, medium, and small melons be $V_{\text {large }}, V_{\text {medium }}$, and $V_{\text {small }}$ respectively. Then, by the formula for the volume of a sphere, we have
$$
\begin{array}{l}
V_{\text {large }}: V_{\text {medium }}: V_{\text {small }}=1:\left(\frac{3}{4}\right)^{3}:\left(\frac{3}{4} \times \frac{4}{5}\right)^{3} \\
=20^{3}: 15^{3}: 12^{3} . \\
\text { Therefore, } V_{\text {large }}>2 V_{\text {medium }}>3 V_{\text {small. }} .
\end{array}
$$