\(\displaystyle{f}'{\left({x}\right)}={5}{x}^{{{4}}}+{\frac{{{1}}}{{{x}^{{{2}}}}}}'\)

\(\displaystyle={5}{\left({x}^{{{4}}}\right)}'+{\left({x}^{{-{2}}}\right)}'\) Derivative of Sum

\(\displaystyle={20}{x}^{{{4}}}-{2}{x}^{{-{3}}}\) Power Rule

\(f'(x)=20x^{4}-\frac{2}{x^{3}}\)