Yes, V-Ray 3.1 is supported in FP 5.0.5, but not with Max 2016. If i remember well, V-Ray 3.2 was the first version with support for 2016.
A different issue is that you're using V-Ray 3.1 for 2015 in 2016. This combination works because binaries are compatible, but it's not supported by ChaosGroup or Forest Pack.
I'm afraid there is not any other way that upgrading V-Ray.