What is $5^3 - (3^2-5)^3$?
We simplify the expression inside the parentheses first.  Simplifying the exponent first, and then subtracting, we get $3^2-5 = 9 - 5 = 4$.  Then, the whole expression is $5^3 - 4^3$.  Once again simplifying exponents first, we get $125 - 64$, which gives us $\boxed{61}$.