[tex]displaystyle frac{(5ab+a^{-3})^2}{5a^4b^{-2}+b^{-3}}-5a^{-2}b^4=frac{(a^{-3}(5a^4b+1))^2}{b^{-3}(5a^4b+1)}-5a^{-2}b^4=\ \ \ =frac{b^3(5a^4b+1)}{a^6}-frac{5b^4}{a^2}=frac{5a^4b^4+b^3-5a^4b^4}{a^6}=dfrac{b^3}{a^6}[/tex]

[tex]frac{(5ab+a^{-3})^{2}}{5a^{4}b^{-2}+b^{-3}}-5a^{-2}b^{4}=frac{(5ab+frac{1}{a^{3}})^{2}}{5a^{4}*frac{1}{b^{2} }+frac{1}{b^{3}}}-5*frac{1}{a^{2}}*b^{4}}=frac{(frac{5a^{4}b+1 }{a^{3}})^{2}}{frac{5a^{4} }{b^{2}}+frac{1}{b^{3}}}-frac{5b^{4} }{a^{2} }=frac{frac{(5a^{4}b+1)^{2}}{a^{6} }}{frac{5a^{4}b+1 }{b^{3} }}-frac{5b^{4} }{a^{2} }=frac{(5a^{4}b+1)^{2}*b^{3}}{(5a^{4}b+1)*a^{6}}-frac{5b^{4} }{a^{2} }=frac{(5a^{4}b+1)*b^{3}}{a^{6} }-frac{5b^{4} }{a^{2} }=[/tex][tex]=frac{5a^{4}b^{4}+b^{3}-5a^{4}b^{4}}{a^{6}}=frac{b^{3} }{a^{6} }[/tex]