(x+2)^4 - 4(x+2)^2 - 5 = 0

Let y = (x+2)^2. The equation becomes y^2 - 4y - 5 = 0. Factoring gives (y-5)(y+1) = 0. So y=5 or y=-1. Since y = (x+2)^2, y must be non-negative. Thus, (x+2)^2 = 5, which means x+2 = ±√5. Therefore, x = -2 ± √5.