smc

Let $m$ be the mean of the three numbers. Then the least of the numbers is $m-10$ and the greatest is $m+15$. The middle of the three numbers is the median, $5$. So $\frac{1}{3}[(m-10)+5+(m+15)]=m$, which can be solved to get $m=10$. Hence, the sum of the three numbers is $3\cdot 10=\boxed{30}$.