[OC pro]

The 1H NMR is really irritating. The triplets want to be hydrogens on a benzene ring but as far as I can make out that would imply there have to be some doublets nearby!

Why?

Try to add up what you have so far:

benzene compound --> substitution pattern? number of protons on the benzene ring?
bromine somewhere
exchangeable proton --> ?
Singlet or doublet --> ?

Your quintet is actually a septet!!! (plz have a closer look) --> only one functional group shows a clean septet