This question combines knowledge of the Pythagorean Theorem with knowledge of inscribed angles in circles. First consider that, since it is a right triangle, then it has a right angle with side lengths 5 and 12. Since a right angle is inscribed in the circle, then the measure of the arc that it intercepts is double the angle, or 180°. That means that the hypotenuse is actually the diameter of the circle, and half of it will be the radius.
By this point you might already know the answer because this is an extremely common Pythagorean Triple, but in case you don't see it yet:
52 + 122 = c2
25 + 144 = c2
169 = c2
c = 13
The hypotenuse has a length of 13, which is also the diameter. Therefore the radius is half of that, which is 6.5.
