$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}-4x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}-2x^{2}-3x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}-4x^{2}-3x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}4x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{2}+8x\phantom{;}-;x^n;}\phantom{;}5x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-5x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{;;-5x\phantom{;}-10\phantom{;}\phantom{;}-;x^n-;x^n;}-5\phantom{;}\phantom{;}\\\end{array}$

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