jmc

We factor the quadratic, getting $(b+5)(b-3)\le 0$. The expression is equal to $0$ when $b=3\text{ or }-5$. When $b\le -5$ or $b\ge 3$, the quadratic is positive. When $-5\le b\le 3$, the quadratic is non-positive. Therefore, $b=\boxed{-5}$ is the least value of $b$ for which $b^2+2b-15\le 0$.