Back in the day, I had Headway books, lower intermediate and intermediate, and a Upper Intermediate Cutting Edge. I agree on the Cutting Edge. It was usually too much for freshman English majors, or perhaps that was just an inappropriate level. And it's interesting to hear good reports on Headway. Whether good or bad, it seemed repetitive and I didn't use it much. However, I did use the New Headway Teacher's Resource book a lot.
I suppose too it would all have been different if the students had had copies too. Me being the only person in the room with a book made a lot of the exercises heavy going, those rare times I dared.
What does IELTS 5.5 correlate to anyway? Halfway between
6 Competent User
Has generally effective command of the language despite some inaccuracies, inappropriacies and misunderstandings. Can use and understand fairly complex language, particularly in familiar situations.
5 Modest user
Has partial command of the language, coping with overall meaning in most situations, though is likely to make many mistakes. Should be able to handle basic communication in own field.
So... broadly... Intermediate?