Can I build it with Qt 5 even though can't I?
According to the Quazip web site:

Platforms supported

QuaZIP has been currently tested on the following platforms:

linux-g++ (Ubuntu 11.10, Qt 4.7.4)
freebsd-g++ (Qt 4.0.0
hpux-acc (HP-UX 11.11)
hpux-g++ (HP-UX 11.11)
win32-g++ (MinGW)
win32-msvc2010 (MS VS 2010 Express, Qt 4.8.4)
win32-msvc2010 (Qt Creator, Qt 5.0.1)
win32-msvc2012 (Qt Creator, Qt 5.2.0)
some Symbian version, reportedly

Requirements

Just zlib and Qt 4/5. Well, Qt 4 depends on zlib anyway, but you will need zlib headers to compile QuaZIP. With Qt5 sometimes you need the zlib library as well (on Windows, for example).
So it appears to be compatible with both Qt 4 and 5; you may have to edit your Qt Creator configuration so it finds the right locations for include files. The Quazip site does have a "Building, testing, and installing" section with some guidelines.

It's an open-source project, so you should expect to have to do some additional work to get it built and usable.