$\begin{array}{l}\phantom{\phantom{;}x^{2}-4x\phantom{;}+5;}{\phantom{;}2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-4x\phantom{;}+5\overline{\smash{)}\phantom{;}2x^{3}-5x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}+5;}\underline{-2x^{3}+8x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+8x^{2}-10x\phantom{;};}\phantom{;}3x^{2}-10x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}+5-;x^n;}\underline{-3x^{2}+12x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;-3x^{2}+12x\phantom{;}-15\phantom{;}\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}-16\phantom{;}\phantom{;}\\\end{array}$

$2x+3+\frac{2x-16}{x^2-4x+5}$