$\begin{array}{l}\phantom{\phantom{;}5x\phantom{;}+3;}{\phantom{;}3x^{2}-5x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}5x\phantom{;}+3\overline{\smash{)}\phantom{;}15x^{3}-16x^{2}-5x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}5x\phantom{;}+3;}\underline{-15x^{3}-9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-15x^{3}-9x^{2};}-25x^{2}-5x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x\phantom{;}+3-;x^n;}\underline{\phantom{;}25x^{2}+15x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}25x^{2}+15x\phantom{;}-;x^n;}\phantom{;}10x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x\phantom{;}+3-;x^n-;x^n;}\underline{-10x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;-10x\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n;}-7\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-5x+2+\frac{-7}{5x+3}$