$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-5;}{\phantom{;}x^{4}+5x^{3}+25x^{2}+125x\phantom{;}+625\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-5\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-5;}\underline{-x^{5}+5x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+5x^{4};}\phantom{;}5x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n;}\underline{-5x^{4}+25x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{4}+25x^{3}-;x^n;}\phantom{;}25x^{3}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n;}\underline{-25x^{3}+125x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-25x^{3}+125x^{2}-;x^n-;x^n;}\phantom{;}125x^{2}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n-;x^n;}\underline{-125x^{2}+625x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-125x^{2}+625x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}625x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n-;x^n-;x^n;}\underline{-625x\phantom{;}+3125\phantom{;}\phantom{;}}\\\phantom{;;;;-625x\phantom{;}+3125\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}3141\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+5x^{3}+25x^{2}+125x+625+\frac{3141}{x-5}$