$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}5x^{4}-8x^{3}+17x^{2}-36x\phantom{;}+73\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}5x^{5}+2x^{4}+x^{3}-2x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-5x^{5}-10x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{5}-10x^{4};}-8x^{4}+x^{3}-2x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}8x^{4}+16x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{4}+16x^{3}-;x^n;}\phantom{;}17x^{3}-2x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-17x^{3}-34x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-17x^{3}-34x^{2}-;x^n-;x^n;}-36x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}36x^{2}+72x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}36x^{2}+72x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}73x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-73x\phantom{;}-146\phantom{;}\phantom{;}}\\\phantom{;;;;-73x\phantom{;}-146\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-149\phantom{;}\phantom{;}\\\end{array}$

$5x^{4}-8x^{3}+17x^{2}-36x+73+\frac{-149}{x+2}$