$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}-5;}{-a^{4}-8a^{3}-42a^{2}-214a\phantom{;}-1069\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}-5\overline{\smash{)}-a^{5}-3a^{4}-2a^{3}-4a^{2}+a\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}-5;}\underline{\phantom{;}a^{5}-5a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}a^{5}-5a^{4};}-8a^{4}-2a^{3}-4a^{2}+a\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-5-;x^n;}\underline{\phantom{;}8a^{4}-40a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}8a^{4}-40a^{3}-;x^n;}-42a^{3}-4a^{2}+a\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-5-;x^n-;x^n;}\underline{\phantom{;}42a^{3}-210a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}42a^{3}-210a^{2}-;x^n-;x^n;}-214a^{2}+a\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-5-;x^n-;x^n-;x^n;}\underline{\phantom{;}214a^{2}-1070a\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}214a^{2}-1070a\phantom{;}-;x^n-;x^n-;x^n;}-1069a\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-5-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}1069a\phantom{;}-5345\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}1069a\phantom{;}-5345\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-5351\phantom{;}\phantom{;}\\\end{array}$

$-a^{4}-8a^{3}-42a^{2}-214a-1069+\frac{-5351}{a-5}$