Selecting Qt5 using qtchooser

The question is, before I try to build supercollider from source, making sure that I am using Qt5. Problem is this:

jsimon@edgy:~$ qmake -v
qmake: could not exec '/usr/lib/x86_64-linux-gnu/qt4/bin/qmake': No such file or directory
jsimon@edgy:~$ locate qmake
/usr/bin/qmake

I think is there something misconfigured with qtchooser, docs here:

Qtchooser man page

and here:

Qtchooser on Linux from Scratch

More digging, there is a directory with some symlinks in it:

jsimon@edgy:/usr/lib/x86_64-linux-gnu/qtchooser$ ls -al
lrwxrwxrwx   1 root root    50 Sep  1 06:04 4.conf -> ../../../share/qtchooser/qt4-x86_64-linux-gnu.conf
lrwxrwxrwx   1 root root    50 Sep  1 06:04 5.conf -> ../../../share/qtchooser/qt5-x86_64-linux-gnu.conf
lrwxrwxrwx   1 root root    50 Sep  1 06:04 qt4.conf -> ../../../share/qtchooser/qt4-x86_64-linux-gnu.conf
lrwxrwxrwx   1 root root    50 Sep  1 06:04 qt5.conf -> ../../../share/qtchooser/qt5-x86_64-linux-gnu.conf

And another deeper directory with what looks to me like the problem, a symlink giving Qt4 as the default:

jsimon@edgy:/usr/lib/x86_64-linux-gnu/qt-default/qtchooser$ ls -al
lrwxrwxrwx 1 root root   53 Sep  1 06:04 default.conf -> ../../../../share/qtchooser/qt4-x86_64-linux-gnu.conf

Some information from qtchooser:

jsimon@edgy:~$ qtchooser -print-env
QT_SELECT="default"
QTTOOLDIR="/usr/lib/x86_64-linux-gnu/qt4/bin"
QTLIBDIR="/usr/lib/x86_64-linux-gnu"

Looking at this page, it ought to be simple:

Handling Multiple Qt Versions

However:

jsimon@edgy:~$ export QT_SELECT=qt5
jsimon@edgy:~$ printenv
[snip]
QT_SELECT=qt5
[snip]
jsimon@edgy:~$ qmake -v
qmake: could not exec '/usr/lib/x86_64-linux-gnu/qt5/bin/qmake': No such file or directory

Back where we're started, no change. Now what?