\((2x^3-21x^2+67x-60):\left(x-5\right)\)
\(=(2x^3-10x^2-11x^2+55x+12x-60):\left(x-5\right)\)
\(=[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)]:\left(x-5\right)\)
\(=\left(x-5\right)\left(2x^2-11x+12\right):\left(x-5\right)\)
\(=2x^2-11x+12\)