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

$5x+5+\frac{2x-8}{x^2-x+1}$