Hard geometry

Circumradius =     [product of the sides ] /  [ 4 * area ]

Since we have a right triangle the area is easy  =  (1/2)(product of the legs)  =  (1/2)(60)  =  30

Product of the sides  = 5*12*13  =  780

Circumradius  =     780  / [ 4 * 30 ]   =  780 / 120  =    6.5

This brings up an important point :  In a right triangle the circumradius =  (1/2) ( hypotenuse)

So :   (1/2) (13)   = 6.5

(13*5*12)/sqrt((13+5+12)*(5-13+12)*(13-5+12)*(13+5-12)) using circumradius formula:

you get 6.5