\(-12\cdot\left(x-5\right)+7\cdot\left(3-x\right)=5\)
\(-12\left(x-5\right)+7\left(-x+3\right)=5\)
\(-\left(12x-12\cdot5\right)+\left(-7x+7\cdot3\right)=5\)
\(-\left(12x-60\right)+\left(-7x+21\right)=5\)
\(-12+60+-7x+21=5\)
\(-12x-7x+0+21=5\)
\(-19+81=5\)
\(\left(-19x+81\right)+\left(-81\right)=5+\left(-81\right)\)
\(-19x+81-81=5-81\)
\(-19x=76\)
\(\frac{19x}{19}=\frac{76}{19}\)
\(x=\frac{2^2\cdot19}{19}\)
\(x=2^2=4\)