Nutanix doesn’t do any tests on incompatible PE-PC combinations, so we cannot guarantee that it will work. It is possible that you may have all sorts of issues. Most common issues are disconnected clusters in the PC and it is possible that you will not be able to manage your cluster from the PC.
I would recommend to upgrade the PE first. There is no valid reason to stay on the version 5.11.x which is already EOL and not supported. All upgrades are non-disruptive to the production, so they can be done any time.