\(\left(x+2\right)\left(x+5\right)< 0\)
\(\Rightarrow\left\{{}\begin{matrix}x+2< 0\\x+5< 0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x< -2\\x< -5\end{matrix}\right.\)
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2< 0\\x+5< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2>0\\x+5>0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< -2\\x< -5\end{matrix}\right.\\\left\{{}\begin{matrix}x>-2\\x>-5\end{matrix}\right.\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x< -5\\x>-2\end{matrix}\right.\)
