\(\left(x+1\right)\left(2x-2\right)-3>-5x-\left(2x+1\right)\left(3x-x\right)\)
\(\Leftrightarrow2x^2-2x+2x-2-3>-5x-\left(6x^2-2x^2+3x-x\right)\)
\(\Leftrightarrow2x^2-2x+2x-5>-5x-6x^2+2x^2-3x+x\)
\(\Leftrightarrow2x^2-5+5x+6x^2-2x^2+3x-x>0\)
\(\Leftrightarrow6x^2-2x>5\)
\(\Leftrightarrow2x\left(3x-1\right)>5\)
\(\Leftrightarrow\left[{}\begin{matrix}2x>5\\3x-1>5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{5}{2}\\x>2\end{matrix}\right.\)
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