\(\left|x-5\right|-2=\left|-7\right|+1\)
\(\Leftrightarrow\left|x-5\right|=7+1+2\)
\(\Leftrightarrow\left|x-5\right|=10\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=10\left(x\ge0\right)\\x-5=-10\left(x< 0\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=15\\x=-5\end{matrix}\right.\)(thỏa đk)