Discovered a dedicated Linux Mint 19 repository on the openSUSE server (there isn’t a really working link but if you tinker a bit with the direct download link you can get to it and make a shell script with following contents:
#!/bin/bash
wget http://download.opensuse.org/repositories/isv:/ownCloud:/desktop/Linux_Mint_19/Release.key -O Release.key
sudo apt-key add - < Release.key
rm Release.key
sudo sh -c "echo 'deb http://download.opensuse.org/repositories/isv:/ownCloud:/desktop/Linux_Mint_19/ /' > /etc/apt/sources.list.d/isv:ownCloud:desktop.list"
sudo apt-get update
sudo apt-get install owncloud-client
You can name it, e. g., add-owncloud-repository, make it executable (chmod u+x add-owncloud-repository), and save it somewhere on your $PATH (e. g. $HOME/bin). Then run it (add-owncloud-repository) and you should have your ownCloud specially tailored for Linux Mint 19.
OK, but this whole thing didn’t work for me because the problem with the libQt5Core library still persists.