\(\left(x-3\right)\left(x-5\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3>0\\x-5< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3< 0\\x-5>0\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}3< x< 5\\\left\{{}\begin{matrix}x>3\\x< 5\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow3< x< 5\)