Mirror image of a parabola wrt a line

Let the curve $C$ be the mirror image of the parabola $y^2 = 4x$ with respect to the line $x + y + 4 = 0.$ If $A$ and $B$ are the points of intersection of $C$ with the line $y = -5$ , then the distance between $A$ and $B$ is?

Problem courtesy: JEE Advanced 2015