\(\left(x-3\right)\left(x+5\right)+\left(x^2-25\right)=0\)\(0\Rightarrow\left(x-3\right)\left(x+5\right)+\left(x-5\right)\left(x+5\right)=0\)
\(\Rightarrow\)\(\left(x+5\right)\left(x-3+x-5\right)=0\)\(\Rightarrow\)\(\left(x+5\right)\left(2x-8\right)=0\)
\(\Rightarrow\)\(\orbr{\begin{cases}x+5=0\\2x-8=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=-5\\x=4\end{cases}}\)