The object distance is equal to image distance in a plane mirror.

For the distance of man from his image to be 5m-

The distance of man from mirror+ distance of image from the mirror= 5m

Since object distance= image distance

Therefore, 2*distance of man from the mirror= 5m

Distance of man from the mirror= 5/2 = 2.5m

The man is 10m from the mirror at the starting, so he will have to walk 10 – 2.5 =7.5m towards the mirror for being 5m away from his image.