Question

$5 x^{x}= \sqrt[3]{5}$

Answer 1

$5 x^{2} =\sqrt[3]{5} \\ \\ x^2=\frac{\sqrt[3]5}{5} \\ \\ x^2=\frac{5^{\frac{1}{3}}}{5} \\ \\ x^{2} =5^{\frac{1}{3}-1} \\ \\ x^2=5^{-\frac{2}{3}} \\ \\ x=+-(5^{-\frac{2}{3}})^{\frac{1}{2}} \\ \\ x=+-5^{-\frac{1}{3}} \\ \\ \boxed{x=+-\frac{1}{\sqrt[3]5}}$