If you use Ubuntu, first uninstall Canonical’s version of Qt, which was developed to support it’s now-defunct phone product.
Uninstall using the Software Center. Then look under your home directory for any folders beginning with ‘Qt’. Manually delete these files & directories, reboot to rebuild the filename ndex database (though technically not necessary for Qt install).
Then install the official Qt version from here: https://www.qt.io/download/
NOTE 2017 Oct 12: This thread is outdated. Not necessary to uninstall Qt. See Install Qt 5 on Ubuntu - Qt Wiki for latest information.