Is the mouse Bluetooth 4.0 or something like that? I would think it would be backward compatible with older versions but maybe that could be the issue?
The mouse is advertised as compatible with Android tablets 3.1+. It has to be 5.1.1, once you throw in a couple "Stupid Me" moments.
I have another Bluetooth mouse I bought in 2008 to use with my HTC Mogul cell phone. It was working with the Nexus but then quit. Erroneously, I
"assumed" it died, and bought a new one, and it didn't work. Exactly which came first, Lollipop of some flavor or my assumption, I simply have no idea. This was one "Stupid Me" moment.
The other "Stupid Me" moment was forgetting my iMac has Bluetooth. I could/should have checked the old mouse using the Mac. I checked the old mouse, and it worked. As did the new mouse. The iMac even saw the Nexus, although I didn't try to pair it up. Have no need for that as I have the Nexus, iMac, and 3 Windows computers all on the home network.
It occurred to me while writing this message, an issue with the file manager software I'm having in connecting to the Nexus may be a Lollipop issue also. It's something I'll have to check out.
I think I'm going to go back to 4.4(?) as my next major step in solving the problem. That will have to wait a bit before I can get to it.