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} $.