$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{4}-4x^{3}+4x^{2}-13x\phantom{;}+27\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{5}\phantom{-;x^n}-4x^{3}-5x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{5}-4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}-4x^{4};}-4x^{4}-4x^{3}-5x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}4x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{4}+8x^{3}-;x^n;}\phantom{;}4x^{3}-5x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-4x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{3}-8x^{2}-;x^n-;x^n;}-13x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}13x^{2}+26x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}13x^{2}+26x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}27x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-27x\phantom{;}-54\phantom{;}\phantom{;}}\\\phantom{;;;;-27x\phantom{;}-54\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-60\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}-4x^{3}+4x^{2}-13x+27+\frac{-60}{x+2}$