jmc

A real number $x$ is in the domain of $h$ if and only if $25-x^2$ and $-(x-2)$ are both nonnegative.

The solutions to $25-x^2\ge 0$ are given by $-5\le x\le 5$.

The solutions to $-(x-2)\ge 0$ are given by $x\le 2$.

The overlap of these solution sets is the interval $[-5,2]$, which has width $\boxed{7}$.