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