\[x^{5}y\left( y^{4} + xy^{5} - x^{2}y^{6} + x^{3}y^{7} \right) =\]
\[= x^{5}y^{5} + x^{6}y^{6} - x^{7}y^{7} + x^{8}y^{8} =\]
\[= x^{8}y^{8} - x^{7}y^{7} + x^{6}y^{6} + x^{5}y^{5}.\]