$\begin{array}{l}\phantom{\phantom{;}m\phantom{;}+5;}{\phantom{;}m^{3}-5m^{2}+25m\phantom{;}-125\phantom{;}\phantom{;}}\\\phantom{;}m\phantom{;}+5\overline{\smash{)}\phantom{;}m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+625\phantom{;}\phantom{;}}\\\phantom{\phantom{;}m\phantom{;}+5;}\underline{-m^{4}-5m^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-m^{4}-5m^{3};}-5m^{3}\phantom{-;x^n}\phantom{-;x^n}+625\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+5-;x^n;}\underline{\phantom{;}5m^{3}+25m^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5m^{3}+25m^{2}-;x^n;}\phantom{;}25m^{2}\phantom{-;x^n}+625\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+5-;x^n-;x^n;}\underline{-25m^{2}-125m\phantom{;}\phantom{-;x^n}}\\\phantom{;;-25m^{2}-125m\phantom{;}-;x^n-;x^n;}-125m\phantom{;}+625\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}125m\phantom{;}+625\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}125m\phantom{;}+625\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1250\phantom{;}\phantom{;}\\\end{array}$

$m^{3}-5m^{2}+25m-125+\frac{1250}{m+5}$