My five year old did the same thing his first time shooting a rifle. Santa brought him a Henry Mini-Bolt .22 lr for Christmas last year.
The first day shooting we spent some time shooting targets and clays, working on sighting and shooting basics. He seemed to catch on really fast. Before we left the range, I put two squirrel targets up at 20 yards. I told him we each get one chance for at a head shot with his rifle.
Needless to say, he nailed his dead center and mine was off an inch and a half. I still say that rifle is too small for me to shoot! I really could not have been happier.