\(\left(x-3\right)\left(x-4\right)=\left(x-5\right)^2\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)-\left(x-5\right)^2=0\)
\(\Leftrightarrow x^2-4x-3x+12-\left(x^2-10x+25\right)=0\)
\(\Leftrightarrow x^2-4x-3x+12-x^2+10x-25=0\)
\(\Rightarrow3x-13=0\)
\(\Rightarrow3x=13\)
\(\Rightarrow x=\frac{13}{3}\)