$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+5;}{\phantom{;}x^{2}+7x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{4}+6x^{3}+5x^{2}-4x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5;}\underline{-x^{4}+x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3}-5x^{2};}\phantom{;}7x^{3}\phantom{-;x^n}-4x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5-;x^n;}\underline{-7x^{3}+7x^{2}-35x\phantom{;}\phantom{-;x^n}}\\\phantom{;-7x^{3}+7x^{2}-35x\phantom{;}-;x^n;}\phantom{;}7x^{2}-39x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5-;x^n-;x^n;}\underline{-7x^{2}+7x\phantom{;}-35\phantom{;}\phantom{;}}\\\phantom{;;-7x^{2}+7x\phantom{;}-35\phantom{;}\phantom{;}-;x^n-;x^n;}-32x\phantom{;}-34\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+7x+7+\frac{-32x-34}{x^2-x+5}$