$\begin{array}{l}\phantom{\phantom{;}x^{2}+5;}{\phantom{;}3x^{2}+5x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+5\overline{\smash{)}\phantom{;}3x^{4}+5x^{3}\phantom{-;x^n}\phantom{-;x^n}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+5;}\underline{-3x^{4}\phantom{-;x^n}-15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-15x^{2};}\phantom{;}5x^{3}-15x^{2}\phantom{-;x^n}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+5-;x^n;}\underline{-5x^{3}\phantom{-;x^n}-25x\phantom{;}\phantom{-;x^n}}\\\phantom{;-5x^{3}-25x\phantom{;}-;x^n;}-15x^{2}-25x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+5-;x^n-;x^n;}\underline{\phantom{;}15x^{2}\phantom{-;x^n}+75\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}15x^{2}+75\phantom{;}\phantom{;}-;x^n-;x^n;}-25x\phantom{;}+70\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+5x-15+\frac{-25x+70}{x^2+5}$