Right, first things first. You said he was banned 5 years ago but you didn't mention how long his ban was for. If his driving ban has expired, then when he makes an application for his driving licence, he would be notified if he needs to do a medical test. If the DVLA thinks the medical is important before returning his licence, he will get confirmation what needs to be done next.
The DVLA medical for drink drivers start with the GP of the person concerned. The medical is based on liver function tests and it's hard to tell whether he should completely abstained from alcohol without knowing how badly your boyfriend's liver is affected. Therefore he will need to take it a step at a time. If the ban is over, then apply for the licence straight away. If a medical is required, ask his to consult his GP to know where he stands.