$\begin{array}{l}\phantom{\phantom{;}5x^{2}+2x\phantom{;}-1;}{\phantom{;}5x^{3}-3x^{2}+5x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}5x^{2}+2x\phantom{;}-1\overline{\smash{)}\phantom{;}25x^{5}-5x^{4}+14x^{3}+8x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}5x^{2}+2x\phantom{;}-1;}\underline{-25x^{5}-10x^{4}+5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-25x^{5}-10x^{4}+5x^{3};}-15x^{4}+19x^{3}+8x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x^{2}+2x\phantom{;}-1-;x^n;}\underline{\phantom{;}15x^{4}+6x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}15x^{4}+6x^{3}-3x^{2}-;x^n;}\phantom{;}25x^{3}+5x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x^{2}+2x\phantom{;}-1-;x^n-;x^n;}\underline{-25x^{3}-10x^{2}+5x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-25x^{3}-10x^{2}+5x\phantom{;}-;x^n-;x^n;}-5x^{2}+5x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x^{2}+2x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{\phantom{;}5x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}5x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}7x\phantom{;}+3\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}-3x^{2}+5x-1+\frac{7x+3}{5x^2+2x-1}$