Glasgow has more students than any city outside of London, and several institutions (the University of Glasgow, Strathclyde University, Caledonian University, the Glasgow School of Art, the Royal Conservatoire of Scotland and a couple of Univ West of Scotland campuses within a few miles) in much the same part of the city- it also has more pubs, clubs, shops, parks and transport links than anywhere except London. Edinburgh is similar-ish in some respects, and while Manchester only has two universities, they're both massive in terms of student numbers.
I also don't think you can limit it to five. Some cities are smaller and have a higher concentration of students, some have parts of the city that are student dominated and parts less so. There are certainly plenty of areas in Glasgow, Edinburgh, Bristol and Manchester that are nothing like what one would typically call a student city.