$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}4x^{3}-20x^{2}+104x\phantom{;}-523\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}4x^{4}\phantom{-;x^n}+4x^{2}-3x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-4x^{4}-20x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}-20x^{3};}-20x^{3}+4x^{2}-3x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}20x^{3}+100x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}20x^{3}+100x^{2}-;x^n;}\phantom{;}104x^{2}-3x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-104x^{2}-520x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-104x^{2}-520x\phantom{;}-;x^n-;x^n;}-523x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}523x\phantom{;}+2615\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}523x\phantom{;}+2615\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}2606\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}-20x^{2}+104x-523+\frac{2606}{x+5}$