Legs of a right triangle are 5 and x+2 and x+3 what is the perimeter

Normally for a right angle triangle we refer to the three sides as consisting of two right angle legs and the hypotenuse. The fact that you described it as having three legs, without defining which is the hypotenuse, makes it an interesting problem.

I suggest that you use the Pythagorian Theorem, first with 5 as the hypotenuse and then with 5 as one leg and (x+3) as the hypotenuse. You know the (x+2) leg can't be the hypotenuse as the hypotenuse is always the longest side, and (x+2) is less than (x+3). Solve for x in both cases. Then you can add the lengths of all three sides to get the perimeter.