The system might have different meta packages that handle the default. For example on Debian there is a
qt4-default and a qt5-default package, installing one of them will uninstall the other and set the symlinks appropriately
$ qtchooser -list-versions
4
5
default
opt-qt55
qt4-i386-linux-gnu
qt4
qt5-i386-linux-gnu
qt5
Then you create QT_SELECT environment variable and set e.g. export QT_SELECT=4 or export QT_SELECT=5.