$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{-5x^{3}+4x^{2}-6x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}-5x^{4}-6x^{3}+2x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{\phantom{;}5x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}5x^{4}+10x^{3};}\phantom{;}4x^{3}+2x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{-4x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{3}-8x^{2}-;x^n;}-6x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{2}+12x\phantom{;}-;x^n-;x^n;}\phantom{;}13x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-13x\phantom{;}-26\phantom{;}\phantom{;}}\\\phantom{;;;-13x\phantom{;}-26\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-24\phantom{;}\phantom{;}\\\end{array}$

$-5x^{3}+4x^{2}-6x+13+\frac{-24}{x+2}$