Answer: D

Small Hint:

Let the legs be $a,b$ and place the right angle at their common endpoint

Big Hint:

The two median lengths give $a^2+\frac{b^2}{4}=25$ and $\frac{a^2}{4}+b^2=40$

Solution:

Let the legs be $a,b.$ The medians from their opposite acute vertices have squared lengths $$a^2+\frac{b^2}{4}=25,\qquad \frac{a^2}{4}+b^2=40.$$ Solving gives $a^2=16$ and $b^2=36.$ Thus the hypotenuse $c$ satisfies $$c^2=a^2+b^2=52,$$ so $c=2\sqrt{13}.$

Thus, the correct answer is D.