Answer
$y^{5}(y^{2}+1)(y-1)(y+1)$
Work Step by Step
$ y^{9}-y^{5}\qquad$...factor out the common term, $y^{5}$
$=y^{5}(y^{4}-1)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=y^{5}(y^{2}-1)(y^{2}+1)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=y^{5}(y^{2}+1)(y-1)(y+1)$