Let x be the distance from the light to the wall on which the mirror is mounted. Then the distance from the person to the wall is 5x. Also let y be the component of distance parallel to the wall from the light to the point on the mirror that the light reaches before hitting the person. The light bulb is therefore be located at (x, y) with respect to this point and the person at (5x, -5y).
Let θ be the angle with respect to the normal at which the light strikes the mirror and reflects to the person. Then
tan θ = y/x. The total distance traveled by the reflected ray is therefore