In a plane mirror the image is virtual. It appears the same distance behind the mirror as the object is in front and that is the law of reflection.
Therefore, to have 5 meter distance between him and the image, the virtual distance of the virtual image behind the mirror should be equal to the real distance between the man and mirror . Therefore the man sholul stand 5/2 meter before the mirror to have 5 feet distance between him and his image. That meanes he should walk by another 7.5 meter towards the mirror in a direction perpendicular to the mirror surface or along the line of man and image line.
The distance of an object from its image in a plane mirror is exactly double the distance of the object from the mirror.
Thus for the man to be 5 meters away from his image he should be at a distance half of that>
Therefore required distance of man from mirror = 5/2 = 2.5 m
Original distance of man from mirror = 10 m (given)
Difference in original and required distance = 10 - 2.5 = 7.5 m.
The man must walk 7.5 m towards the mirror to be 5 m away from his image.