Answer
$625 a^4 - 1000 a^3 b + 600 a^2 b^2 - 160 a b^3 + 16 b^4$
Work Step by Step
Using the Binomial Formula, the expression $
(5a-2b)^4
$ expands to
\begin{array}{l}
(5a)^4(-2b)^0+
\dfrac{4}{1!}(5a)^3(-2b)^1+
\dfrac{4\cdot4}{2!}(5a)^2(-2b)^2+\\
\dfrac{4\cdot4\cdot3\cdot2}{3!}(5a)^1(-2b)^3+
\dfrac{4\cdot4\cdot3\cdot2\cdot1}{4!}(5a)^0(-2b)^4
\\\\=
625 a^4 - 1000 a^3 b + 600 a^2 b^2 - 160 a b^3 + 16 b^4
\end{array}