$\begin{array}{l}\phantom{\phantom{;}x^{2}+5x\phantom{;}+5;}{\phantom{;}x^{2}-5x\phantom{;}+20\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+5x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+5x\phantom{;}+5;}\underline{-x^{4}-5x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-5x^{3}-5x^{2};}-5x^{3}-5x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+5x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{3}+25x^{2}+25x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+25x^{2}+25x\phantom{;}-;x^n;}\phantom{;}20x^{2}+25x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+5x\phantom{;}+5-;x^n-;x^n;}\underline{-20x^{2}-100x\phantom{;}-100\phantom{;}\phantom{;}}\\\phantom{;;-20x^{2}-100x\phantom{;}-100\phantom{;}\phantom{;}-;x^n-;x^n;}-75x\phantom{;}-98\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-5x+20+\frac{-75x-98}{x^2+5x+5}$