$${ x }^{ 4 } +5 { x }^{ 3 } { y }^{ 2 } +xy+5 { y }^{ 3 }$$
Factor
$\left(x+5y^{2}\right)\left(x^{3}+y\right)$
Solution Steps
Do the grouping $x^{4}+5x^{3}y^{2}+xy+5y^{3}=\left(x^{4}+5x^{3}y^{2}\right)+\left(xy+5y^{3}\right)$, and factor out $x^{3}$ in the first and $y$ in the second group.
