$\begin{array}{l}\phantom{\phantom{;}x^{2}+5;}{\phantom{;}4x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+5\overline{\smash{)}\phantom{;}4x^{3}-5x^{2}+x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+5;}\underline{-4x^{3}\phantom{-;x^n}-20x\phantom{;}\phantom{-;x^n}}\\\phantom{-4x^{3}-20x\phantom{;};}-5x^{2}-19x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+5-;x^n;}\underline{\phantom{;}5x^{2}\phantom{-;x^n}+25\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}5x^{2}+25\phantom{;}\phantom{;}-;x^n;}-19x\phantom{;}+32\phantom{;}\phantom{;}\\\end{array}$

$4x-5+\frac{-19x+32}{x^2+5}$