$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-5;}{\phantom{;}x^{3}+5x^{2}+20x\phantom{;}+100\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-5\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-5x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-5;}\underline{-x^{4}+5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+5x^{3};}\phantom{;}5x^{3}-5x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n;}\underline{-5x^{3}+25x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{3}+25x^{2}-;x^n;}\phantom{;}20x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n;}\underline{-20x^{2}+100x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-20x^{2}+100x\phantom{;}-;x^n-;x^n;}\phantom{;}100x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n-;x^n;}\underline{-100x\phantom{;}+500\phantom{;}\phantom{;}}\\\phantom{;;;-100x\phantom{;}+500\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}504\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+5x^{2}+20x+100+\frac{504}{x-5}$