\((2x-1)^7=(2x-1)^5\)
\(\Rightarrow\left(2x-1\right)^7-\left(2x-1\right)^5=0\)
\(\Rightarrow\left(2x-1\right)^5\cdot\left[\left(2x-1\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x-1\right)^5=0\\\left(2x-1\right)^2-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=1\\2x-1=1\\2x-1=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\2x=2\\2x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=0\end{matrix}\right.\)
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