#### Answer

$(8m+5n)(8m-5n)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
64m^2-25n^2
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
64m^2
$ and $
25n^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
64m^2-25n^2
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(8m)^2-(5n)^2
\\\\=
(8m+5n)(8m-5n)
.\end{array}