\(\left(5x-2\right)^4=81\)
=>\(\left(5x-2\right)^4=3^4=\left(-3\right)^4\)
=>\(\left[{}\begin{matrix}5x-2=3\\5x-2=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=5\\5x=-1\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{5}\end{matrix}\right.\)