Answer
$5y^{2}(y-1)(y-2)(y+2)$
Work Step by Step
$ 5y^{5}-5y^{4}-20y^{3}+20y^{2}\qquad$...factor in pairs.
$=(5y^{5}-5y^{4})+(-20y^{3}+20y^{2})$
$=5y^{4}(y-1)-20y^{2}(y-1)\qquad$...factor out the common expression
$=(y-1)(5y^{4}-20y^{2})\qquad$...factor again
$=(y-1)[5y^{2}(y^{2}-4)]\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=(y-1)[5y^{2}(y-2)(y+2)]$
$=5y^{2}(y-1)(y-2)(y+2)$
