Here is a quick install for the latest version of the owncloud client on Linux Mint 18:
sudo apt-key add - < Release.key
sudo sh -c "echo 'deb https://download.owncloud.org/download/repositories/8.2/Ubuntu_16.04/ /' >> /etc/apt/sources.list.d/owncloud-client.list"
sudo apt update
sudo apt install owncloud-client
The “Depends: ocqt562-libqt5gui5 but it is not going to be installed” problem
Many people report issues similar to this here:
libowncloudsync0 : Depends: ocqt562-libqt5core5a but it is not going to be installed
Depends: ocqt562-libqt5gui5 but it is not going to be installed
Depends: ocqt562-libqt5keychain1 but it is not going to be installed
Depends: ocqt562-libqt5network5 but it is not going to be installed
Depends: ocqt562-libqt5widgets5 but it is not going to be installed
It is a know issue and has been discussed in the owncloud client github issues extensively: https://github.com/owncloud/client/issues/6034. It mostly boils down to either an old repo url the /etc/apt/sources.list.d/owncloud-client.list, a faulty prior installation or a combintation of both.
What can you do? Make sure you have only one line in your /etc/apt/sources.list.d/owncloud-client.list. It must look like this
deb https://download.owncloud.org/download/repositories/8.2/Ubuntu_16.04/ /
After you made sure of that, remove whatever parts left of your previous owncloud client and give it a fresh install.
apt purge owncloud-client
apt install -f
apt install owncloud-client
And if it still does not work? Hit the owncloud github and report it as a new issue: https://github.com/owncloud/client/issues