\(\left(x-4\right)^{15}=25\cdot\left(x-4\right)^{13}\\ \Leftrightarrow\left(x-4\right)^{13}\left[\left(x-4\right)^2-25\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\\left(x-4\right)^2=25\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=9\\x=-1\end{matrix}\right.\)