I don't know if your trip is planned out, but you could consider to split the 5 days in BKK to a 2-3 days at each end. Then you can get the tooth prepared and temped w/ the impression taken in BKK, go to Phuket and get the final restoration placed at the end ib BKK before you go. BKK has lots of good dentists.
DC-one The Dental Clinic Thailand. (66-2) 240-2800
Also: Dental Hospital, Sukhumwit Soi 49, or
International Hospital - Bangkok, Thailand - Bumrungrad International, more pricey, but high quality doctors and may be having in house lab tch service.
also : Smile Center
1521/2 Sukhumvit Rd. Between Soi 67 & 69
Prakanong BTS
02-392-2953 02-392-0676 02-381-6512-3
this place's website gives turnaround times that might suit you:
Bangkok Dental Clinic, Thailand Dental Clinic, Teeth Whitening Thailand Dental Clinic, Laser Whitening Thailand Dental Clinic.
and finally:
A Dental Clinic Bangkok Thailand, Dentist Bangkok Thailand, Dental Price and Duration