On Ubuntu 16.04, Qt 5.5.1 is included and used by default. How can I update the system so it uses a newer version, system wide by default (QT 5.7.1 for example)?
Apparently there's a bug in 5.5.1 that is causing an application I'm using to crash. I was encourages to upgrade to a newer version of Ubuntu, which uses a more recent version of QT. But I'd much rather update QT on Ubuntu 16.04 if possible.
You could install Kubuntu 18.04 alongside your current OS. It comes with Qt 5.9.5. Later on, by adding the kubuntu-backports ppa, users could get even newer versions depending on what policy decision the Kubuntu Council takes.
You can't simply upgrade the Qt library to a new version as such. Almost everything that depends on Qt would need to be recompiled against the newer version.
If you want a newer version, an option might be to check out the stable KDE neon.
It might be better to upgrade to Ubuntu 18.04 though, as it is an LTS and also includes Qt 5.9 which is an LTS version of Qt.