$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{5}-5x^{4}+25x^{3}-121x^{2}+605x\phantom{;}-3025\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{6}\phantom{-;x^n}\phantom{-;x^n}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{6}-5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{6}-5x^{5};}-5x^{5}\phantom{-;x^n}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{5}+25x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{5}+25x^{4}-;x^n;}\phantom{;}25x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-25x^{4}-125x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-25x^{4}-125x^{3}-;x^n-;x^n;}-121x^{3}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}121x^{3}+605x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}121x^{3}+605x^{2}-;x^n-;x^n-;x^n;}\phantom{;}605x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n-;x^n;}\underline{-605x^{2}-3025x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-605x^{2}-3025x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-3025x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}3025x\phantom{;}+15125\phantom{;}\phantom{;}}\\\phantom{;;;;;\phantom{;}3025x\phantom{;}+15125\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}15117\phantom{;}\phantom{;}\\\end{array}$

$x^{5}-5x^{4}+25x^{3}-121x^{2}+605x-3025+\frac{15117}{x+5}$