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5m\left(mn+p^{2}\right)+n^{2}\left(mn+p^{2}\right)
Do the grouping 5m^{2}n+5mp^{2}+n^{2}p^{2}+mn^{3}=\left(5m^{2}n+5mp^{2}\right)+\left(n^{2}p^{2}+mn^{3}\right), and factor out 5m in the first and n^{2} in the second group.
\left(mn+p^{2}\right)\left(5m+n^{2}\right)
Factor out common term mn+p^{2} by using distributive property.