Answer
$7xy(x^{2}+y^{2})(x-y)(x+y)$
Work Step by Step
$ 7x^{5}y-7xy^{5}\qquad$... factor out the common term, $7xy$
$=7xy(x^{4}-y^{4})\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=7xy(x^{2}+y^{2})(x^{2}-y^{2})\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=7xy(x^{2}+y^{2})(x-y)(x+y)$
