Answer
$(x-5)^2(x+5)$
Work Step by Step
Using factoring by grouping, the factored form of the given expression, $
x^3-5x^2-25x+125
,$ is
\begin{array}{l}
(x^3-5x^2)-(25x-125)
\\\\=
x^2(x-5)-25(x-5)
\\\\=
(x-5)(x^2-25)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$, the expression above is further factored as
\begin{array}{l}
(x-5)(x+5)(x-5)
\\\\=
(x-5)^2(x+5)
.\end{array}