The Matthews Genesis bows have low draw weight, no draw length, and not too expensive. If you have an Archery in Schools program they also use these bows. Looking into a used one might work too.
At 5 I wouldn't step up into anything more serious unless he gets serious. IIRC my youngest daughter started shooting around 8 or so. She got a hand me down bow I bought used for my older daughter after I upgraded her bow. Also, a more serious bow will have a specific draw length. At his age he might not be tall enough to even fit into a more serious bow.
If you go recurve pay attention to draw weight. It's about all that's going to matter at that age.