I ran this by the developers, and here's what they said:
"[Whether the tracker works with the v5 plugin], may be dependent on the eye tracker firmware version.
Other generic things that can cause connectivity issues with Tobii Eye Trackes on all platforms is firerwalls, etc. Also, on current versions of the macOS/Windows Operating system the network scanning technique used by the old SDK doesn't work well, so they may need to go into the Network Settings and look for the Tobii device and grab it's IP address and use the "/ ipaddress = " attribute of the <eyetracker> element to have it connect. That's probably the lowest hanging fruit possibility for making it work.
Failing that you'd have to check whether or not the firmware on their eye tracker has been updated. I've found that newer Tobii firmware sometimes breaks compatibility with the older SDK's (even older version of the Pro SDK)."
Since the Pro Nano, at least in its current firmware iteration, requires the Tobii Pro SDK, it may be worth checking whether the tracker connects okay using Inquisit 6, which uses the Pro SDK for its plugin, and if so consider upgrading to that version. (Inquisit 5 uses the predecessor SDK.)