Answer
$(z-5p)(z^2+5pz+25p^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
z^3-125p^3
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using $(a\pm b)(a^2\mp ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(z-5p)[(z)^2+z(5p)+(5p)^2]
\\\\=
(z-5p)(z^2+5pz+25p^2)
.\end{array}
