Use the quotient rule to find that f'(x) = 6/(x+6)2.
When does f'(x) = 5?
5 = 6/(x+6)2
One way to solve this is to isolate (x+6)2 = 6/5. Now take the square root of both sides, then subtract 6 to isolate x.
Or you could square the binomial, distribute the 6, set equal to zero and use the quadratic formula or complete the square (after determining that factoring will not work).
Remember when you take the square root of 6/5 , you have to consider both +/-.