My son potty trained a couple months before his second birthday as well. I don't think it's too early, but I do think that your expectations about accidents should probably be different than for a kid who's say, 3 1/2 and just potty trained. Ds will be 3 this summer, so we're coming up on a year of being "potty trained". He does still occasionally have accidents during the day. Most of them are just leaks, not full out pees. He wears the little Gerber brand non-waterproof training pants as underwear. They are really just slightly padded underwear, but it's enough that sometimes I don't have to change his jeans when he has a little accident. The accidents seem to come in little spurts, where he gets lazy/too distracted or whatever to take himself potty when he needs to. After a few accidents, he gets more vigilant about taking himself on time. When we first potty trained him, he was much more amenable to me just watching the clock and taking him when I thought it was time. Now that he's older he's all about being independent and really resists me suggesting that he go potty. I do insist he go potty sometimes, like before we get in the car to run errands and first thing in the morning when he's still kind of groggy and I know he's liable to have accidents. Other than that I try to respect his wishes for taking care of it himself.
I think it's normal for kids who start early to have a longer transition period, and that's okay. I'd still rather wash some soiled underpants a couple times a week than do full out diaper laundry for another year! 5 in a day is a lot though, I'd probably try to take more of the responsibility of making sure he's sitting on the potty regularly if I were you, though if he's already at that strong-willed independent stage that might be difficult.