Th1: \(\left\{ \begin{array}{l} 3\le m\\ m+1\le 5 \end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} 3\le m\\ m\le 4 \end{array} \right .\Leftrightarrow 3\le m\le 4\)
Khi đó \(A\cup B=(3;5)\).
Th2: \(\left\{ \begin{array}{l} m\le 3 \\5\le m+1\end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} 3\le m\\ m\ge 4 \end{array} \right . \text { (loại)}\).