\(2\left(m-1\right)x-m\left(x-1\right)=2\left(m-1\right)+5\)
\(\Leftrightarrow2\left(m-1\right)\left(x-1\right)-m\left(x-1\right)=5\)
\(\Leftrightarrow\left[2\left(m-1\right)-m\right]\left(x-1\right)=5\)
\(\Leftrightarrow\left(m-2\right)\left(x-1\right)=5\)
\(\Rightarrow m\ne2\)