It seems like someone always knows somebody who grew a foot their senior year, or something like that. While it seems a little difficult to believe, my guess is there is enough truth to it that suggests that boys really can have a late, major growth spurt.
Keep in mind that while it seems like so many men are tall, the actual average height for a guy is 5'9.5".
If you kiddos seems healthy and nutritionally well adjusted (and your doctor sees no issues), I'd simply not worry about it, including trying to get the extra calories in him. Remember, healthy eating habits formed now are for life. Encouraging a regimen where he has a high calorie snack or milkshake before bed may seem like a good idea now, but will it be when he is 25, or 30 or 50? My husband's family were big on after school snacks and before bed snacks - he simply cannot break that routine that was established the whole time he was growing up. He is overweight and so are his siblings (but his parents are not - they just had the kids engage in this terrible habit because they were "skinny kids" according to my mother in law). My husband literally cannot walk in the door from work with immediately getting a snack, and cannot go to bed without another snack.
Good luck!