\(\left(2x-3\right)^2-\left(x+5\right)^2=0\)
\(\Leftrightarrow\left(2x-3\right)^2=\left(x+5\right)^2\)
\(\Leftrightarrow\left|2x-3\right|=\left|x+5\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=x+5\\2x-3=-x-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=\frac{-2}{3}\end{matrix}\right.\)