The value of $m$ which changes $m(m+1)=30$into a true statement is

$m(m+1)=30$

when $m=6$

$\begin{array}{l}6(6+1)=30\\ 6\left(7\right)=30\\ 42=30\\ L.H.S\ne R.H.S\end{array}$

When $m=5$

$\begin{array}{l}5(5+1)=30\\ 5\left(6\right)=30\\ 30=30\\ L.H.S=R.H.S\end{array}$

When $m=4$

$\begin{array}{l}m(m+1)=30\\ 4(4+1)=30\\ 4\left(5\right)=30\\ 20=30\\ L.H.S\ne R.H.S\end{array}$

When $m=5$

$\begin{array}{l}-5(-5+1)=30\\ -5(-4)=30\\ 20=30\\ L.H.S=R.H.S\\ \text{If }m=5 \text{then }m(m+1)=30\end{array}$