Using the Law of Cosines we have
5^2 = x^2 + (x + 2)^2 - 2[ x (x +2)] cos (60)
25 = x^2 + x^2 + 4x + 4 - 2 [x^2 + 2x] (1/2)
25 = 2x^2 + 4x + 4 - x^2 - 2x
25 = x^2 + 2x + 4 rearrange as
x^2 + 2x - 21 = 0
Using the quadratic formula, x = √22 - 1 ≈ 3.69