$\begin{array}{l}\phantom{\phantom{;}5x^{2}-12x\phantom{;}+5;}{\frac{1}{5}x^{3}+\frac{\frac{12}{5}}{5}x^{2}+\frac{\frac{119}{25}}{5}x\phantom{;}+\frac{\frac{1128}{125}}{5}\phantom{;}\phantom{;}}\\\phantom{;}5x^{2}-12x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}5x^{2}-12x\phantom{;}+5;}\underline{-x^{5}+\frac{12}{5}x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+\frac{12}{5}x^{4}-x^{3};}\frac{12}{5}x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}5x^{2}-12x\phantom{;}+5-;x^n;}\underline{-2.4x^{4}+\frac{144}{25}x^{3}-2.4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2.4x^{4}+\frac{144}{25}x^{3}-2.4x^{2}-;x^n;}\frac{119}{25}x^{3}-2.4x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}5x^{2}-12x\phantom{;}+5-;x^n-;x^n;}\underline{-4.76x^{3}+\frac{1428}{125}x^{2}-4.76x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-4.76x^{3}+\frac{1428}{125}x^{2}-4.76x\phantom{;}-;x^n-;x^n;}\frac{1128}{125}x^{2}-4.76x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}5x^{2}-12x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{-9.024x^{2}+\frac{13536}{625}x\phantom{;}-9.024\phantom{;}\phantom{;}}\\\phantom{;;;-9.024x^{2}+\frac{13536}{625}x\phantom{;}-9.024\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\frac{10561}{625}x\phantom{;}-9.024\phantom{;}\phantom{;}\\\end{array}$

$\frac{1}{5}x^{3}+\frac{12}{25}x^{2}+\frac{119}{125}x+\frac{1128}{625}+\frac{\frac{10561}{625}x-9.024}{5x^2-12x+5}$