Answer
$(m^2-5)(m^4+5m^2+25)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
m^6-125
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using the factoring of the sum/difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(m^2-5)[(m^2)^2+m^2(5)+(5)^2]
\\\\=
(m^2-5)(m^4+5m^2+25)
.\end{array}
