\(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)

applying the laws of indices

\(2^{5x - x} = 2^{10(1/5)}\)

\(2^{4x} = 2^{10(1/5)}\)

\(2^{4x} = 2^2\)
Equating the powers
then 4x = 2

therefore, x = \(\frac{2}{4}\) = \(\frac{1}{2}\)