I doubt they will (what part of "LTS" implies that they give a darn?).
You could try compiling calibre from scratch, just
checkout the source code and run:
Code:
python2 setup.py bootstrap
sudo python2 setup.py install
Assuming you have all the build-deps for calibre installed (and that they package recent enough versions), it should install just fine.
Linking against the system Qt5 should ensure that no issues arise because of incompatibility with the bundled Qt5 libs.