Yeah, that 5 am departure from CGK is going to be a bit brutal. Up at 3 am - always my favorite...
I see there's a transit hotel in the airport itself, for about US$85, that might make sense. Gets mixed reviews, but it's only for about 8 hours, and you can't beat the location.
The Transit Hotel is on the top floor the Terminal 2 overlooking the apron. Noise should be less of a factor after midnight. Its convenient, just a short walk from International Arrival. The fast food restaurants should be open till 9-10pm. Anyway after a 20+ hours flight from the States, the jetlags normally kept me awake after 2am.