I had a try with EasyVDR 3.5 (Kernel 4.4) and the open source drivers . Indeed the 5580 then works. However, the 5881 then no longer works: it gives a signal, but no picture. The 5881 only seems to work with the closed drivers.
I tried to install the TBS 5580 with the Open Source driver (http://www.tbsdtv.com/download/document/linux/media_build-2018-0206.tar.bz2) on 3.13.0-106-generic (Yavdr). That made my older TBS 5881 USB devices stop working, the 5580 did not seem to work either. Then I installed a new OS : 4.13.0.36-g...