jmc

The expressions inside each square root must be non-negative. Therefore, $x-2\ge 0$, so $x\ge 2$, and $5-x\ge 0$, so $x\le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\boxed{[2,5)}$.