Answer
$5x(x^2+4)(x+2)(x-2)$
Work Step by Step
Factoring the $GCF=
5x
$, then the given expression, $
5x^5-80x
$ is equivalent to
\begin{array}{l}
5x(x^4-16)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the complete factored form of the expression above is
\begin{array}{l}
5x(x^2+4)(x^2-4)
\\\\=
5x(x^2+4)(x+2)(x-2)
.\end{array}
