$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-5;}{\phantom{;}3x^{2}+15x\phantom{;}+75\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-5\overline{\smash{)}\phantom{;}3x^{3}\phantom{-;x^n}\phantom{-;x^n}-35\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-5;}\underline{-3x^{3}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}+15x^{2};}\phantom{;}15x^{2}\phantom{-;x^n}-35\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n;}\underline{-15x^{2}+75x\phantom{;}\phantom{-;x^n}}\\\phantom{;-15x^{2}+75x\phantom{;}-;x^n;}\phantom{;}75x\phantom{;}-35\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n;}\underline{-75x\phantom{;}+375\phantom{;}\phantom{;}}\\\phantom{;;-75x\phantom{;}+375\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}340\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+15x+75+\frac{340}{x-5}$