$\begin{array}{l}\phantom{-a\phantom{;}+1;}{\phantom{;}a^{4}+a^{3}+a^{2}+a\phantom{;}+1\phantom{;}\phantom{;}}\\-a\phantom{;}+1\overline{\smash{)}-a^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{-a\phantom{;}+1;}\underline{\phantom{;}a^{5}-a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}a^{5}-a^{4};}-a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{-a\phantom{;}+1-;x^n;}\underline{\phantom{;}a^{4}-a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}a^{4}-a^{3}-;x^n;}-a^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{-a\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}a^{3}-a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}a^{3}-a^{2}-;x^n-;x^n;}-a^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{-a\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}a^{2}-a\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}a^{2}-a\phantom{;}-;x^n-;x^n-;x^n;}-a\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{-a\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}a\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}a\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$

$a^{4}+a^{3}+a^{2}+a+1$