$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}+5;}{\phantom{;}4x^{2}-4x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}+5\overline{\smash{)}\phantom{;}16x^{3}+4x^{2}\phantom{-;x^n}+19\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}+5;}\underline{-16x^{3}-20x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-16x^{3}-20x^{2};}-16x^{2}\phantom{-;x^n}+19\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}+5-;x^n;}\underline{\phantom{;}16x^{2}+20x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}16x^{2}+20x\phantom{;}-;x^n;}\phantom{;}20x\phantom{;}+19\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}+5-;x^n-;x^n;}\underline{-20x\phantom{;}-25\phantom{;}\phantom{;}}\\\phantom{;;-20x\phantom{;}-25\phantom{;}\phantom{;}-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-4x+5+\frac{-6}{4x+5}$