\(\left(x-5\right)^5=\left(x-5\right)^6\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^5=0\)
\(\Rightarrow\left(x-5\right)^5\left(x-6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)
\(\left(x-5\right)^5=\left(x-5\right)^6\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^5=0\)
\(\Rightarrow\left(x-5\right)^5.\left(x-5-1\right)=0\)
\(\Rightarrow\left(x-5\right)^5.\left(x-6\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x-5\right)^5=0\\x-6=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)