Answer
$(p+5q)(p^2-5pq+25q^2)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of the sum/difference of 2 cubes, then the factored form of the the given expression, $
p^3+125q^3
$, is
\begin{array}{l}
(p+5q)[(p)^2-p(5q)+(5q)^2]
\\\\=
(p+5q)(p^2-5pq+25q^2)
.\end{array}
