\(+,x>2\Rightarrow2x-4>0\Rightarrow\left|2x-4\right|=2x-4\Rightarrow2x-4=4x+5\Leftrightarrow2x=4x+9\Leftrightarrow x=\frac{-9}{2}\left(\text{loại}\right)\)
\(+,x\le2\Rightarrow2x-4\le0\Rightarrow\left|2x-4\right|=4-2x\Rightarrow4-2x=4x+5\Leftrightarrow4=6x+5\Leftrightarrow6x+1=0\Leftrightarrow x=\frac{-1}{6}\left(\text{tm}\right)\)