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m^{2}\left(m-4\right)+5\left(m-4\right)
Do the grouping m^{3}-4m^{2}+5m-20=\left(m^{3}-4m^{2}\right)+\left(5m-20\right), and factor out m^{2} in the first and 5 in the second group.
\left(m-4\right)\left(m^{2}+5\right)
Factor out common term m-4 by using distributive property. Polynomial m^{2}+5 is not factored since it does not have any rational roots.