$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{3}-3x^{2}+3x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}-2x^{3}\phantom{-;x^n}+8x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3};}-3x^{3}\phantom{-;x^n}+8x\phantom{;}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+3x^{2}-;x^n;}\phantom{;}3x^{2}+8x\phantom{;}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-3x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}-3x\phantom{;}-;x^n-;x^n;}\phantom{;}5x\phantom{;}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-5x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;;;-5x\phantom{;}-5\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-20\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-3x^{2}+3x+5+\frac{-20}{x+1}$