regarding the GH5, this might have to do with the brand new and not yet common codec the camera does. But we have just released a new beta version wich has full GH5 support, including 4k and 10bit 422 color sampling. You can download the latest beta version under http://www.tentaclesync.com/#download (Find it in the beta section there)
Since Tentacle Sync Studio depends only on codecs which are installed on the system, you may need to install the Apple Pro Format Codecs to finally get this to work.
To install the codecs, please read this post:
Regarding the not matching tc between GH5 and F5 I need more information from you. Maybe you can upload a screenshot of the loaded in footage and your settings panel in Tentacle Sync Studio?