Answer
$y(y^{2}+9)(y-3)(y+3)$
Work Step by Step
$ y^{5}-81y\qquad$...factor out the common term, $y$
$=y(y^{4}-81)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=y(y^{2}+9)(y^{2}-9)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=y(y^{2}+9)(y-3)(y+3)$