Pitmountainpony - Sleep training does not always involve leaving a baby to cry.
Humphrey you will probably flame me for this but I coslept with my DS3 (my worst sleeper) for periods around the 5m stage and without doubt this made his sleep far far far worse. There is also no way on earth he'd have slept more than 45 minutes when kept in the same room as us during the evening.
I found that when we moved him to his own room he still woke up, a bit, and I went straight away to feed him, but he woke far less than he did when cosleeping, simply because we were not disturbing him.
When cosleeping he'd wake 5-8 times a night.
When in his own room he'd wake say 2-3 times a night, which IMO would be totally normal for a 5mo.
Obviously everyone is different but I preferred getting up those 2-3 times a night, and sitting on a chair in his room to do a feed, because I slept better in between said feeds. When cosleeping I never slept properly, and used to wake feeling like death warmed up, but I fully accept that that's just me, and that others sleep very well with their babies beside them.
Difficult I know because of the SIDS advice, but if you are asking for advice (that doesn't involve CIO) I'd say put him in his own room. I can't advise on reflux though as mine never had it, and in that I will absolutely agree that I was 100% lucky. Reflux must be a living hell for you and LO and I'm really sorry you and DS are having to cope with it.