\(\left(x-5\right)^2=4x^2\)
=>\(\left(2x\right)^2-\left(x-5\right)^2=0\)
=>\(\left(2x-x+5\right)\left(2x+x-5\right)=0\)
=>(x+5)(3x-5)=0
=>\(\left[{}\begin{matrix}x+5=0\\3x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=\dfrac{5}{3}\end{matrix}\right.\)