When simplified, $(-\frac{1}{125})^{-2/3}$ becomes:
$\textbf{(A)}\ \frac{1}{25} \qquad \textbf{(B)}\ -\frac{1}{25} \qquad \textbf{(C)}\ 25\qquad \textbf{(D)}\ -25\qquad \textbf{(E)}\ 25\sqrt{-1}$
To remove the negative exponent, flip the fraction of the base.  This results in $(-125)^{2/3}$.
Then, cube root $-125$ and and square the result to get the answer of $25$, or answer choice $\boxed{\textbf{(C)}}$.