=>\(\left(x-5\right)^{x+1}\left[1-\left(x-5\right)^{12}\right]=0\)
=>\(\orbr{\begin{cases}\left(x-5\right)^{x+1}=0\\1-\left(x-5\right)^{12}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^{12}=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=5\\x-5=\pm1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=5\\x\in\left\{6;4\right\}\end{cases}}}\)