By the external angle of a triangle theorem
m < ABD = m < BDC + m < BCD
That is 5x + 2 = x^2 - 1 + 4x - 3
x^2 + 4x - 5x - 1 - 3 - 2 = 0
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3, -2
x cannot be -2 because that would make the external angle, 5x-2 negative.
Answer x = 3