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

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