Benedryl is a bit sedating to some but it is well tolerated by most 5yo in that setting.
Dosing is up to 1 tsp (5cc) per 25 lb up to every 6 hrs. You can control the discomfort or swelling more naturally by using cold compresses. Wet a face cloth & place it in a ziploc bag & chill in the freezer. Or crush a few ice cubes into the same face cloth , ziploc it & you have easy compress for use.