For some time now it has been possible to compile and use Qt manually on the Red Hat Enterprise Linux platform, but with the later Qt 5 releases it hasn't been as straightforward due to the libraries and tools that come provided with Red Hat Enterprise Linux. Now with the release of Qt 5.5.0, there will be full and official support for Red Hat Enterprise Linux 6.6!
What this actually means is that Qt is tested on Red Hat Enterprise Linux 6.6 along with the other platforms that are CI tested (i.e Qt is regularly built and platform tests are run on a regular basis to try and prevent bugs from being introduced when a change is made), as indicated here http://doc.qt.io/QtSupportedPlatforms/index.html.
In addition to the fact that Red Hat Enterprise Linux 6.6 is now tested much more thoroughly on a regular basis, there will also be a pre-built version of Qt for this platform. This will enable you to download Qt and install it without having to wait for the compilation to succeed. This also means less hassle with setting up all the dependencies and the like to get Qt built.
Since the same rules apply for earlier versions of Red Hat Enterprise Linux, as for any other Linux distribution, Qt will be usable on these platforms, too. As long as you can use a supported compiler version and the dependencies required for building Qt are also available then there is no problem with compiling and developing with Qt on the earlier versions. However, for simplicity and ease of use reasons, we recommend that you consider moving to Red Hat Enterprise Linux 6.6 when switching to Qt 5.5.0.