\(A\cap B=\varnothing\Leftrightarrow\left[{}\begin{matrix}2a\ge5\\3a+1\le0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a\ge\dfrac{5}{2}\\a\le-\dfrac{1}{3}\end{matrix}\right.\)
\(\Rightarrow A\cap B\ne\varnothing\Leftrightarrow-\dfrac{1}{3}< a< \dfrac{5}{2}\)