Answer
True.
Work Step by Step
Plugging in $(6,0)$: $5\cdot6-6\cdot0-30=30-0-30=0$, thus $(6,0)$ is on the line.
If $y=mx+b$ is the equation of a line, then $m$ is the slope.
Hence here: $5x+6y-30=0\\6y=30-5x\\y=5-\frac{5}{6}x$, so $m=-\frac{5}{6}$. Thus the statement is true.
