If it tastes good and you can have it gone in a relatively short time (this week?), then no problem. If you're going to keep some around for a few weeks, I'd suggest refrigerating it and once a week check a bottle for amount of carbonation. If the 'pfft' sounds really strong and/or you get gushing, you are only a short way away from bottle bombs, in which case I would de-cap the entire batch and then sanitize and re-cap. It won't disturb or add O2 to the beer. But still keep it in fridge and recheck occasionally. To bottle-condition at room temp, I always put my bottles in a large plastic tote with a snap-on lid. If anything blows, liquid and broken glass is safely contained.
And for the future, when doing a 5 gal batch Palmer says to use only 3/4 cup of priming sugar for most ales, and not the entire 5 oz. that comes with the kit.