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

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