Mixed clusters is supported, the support is for the upgrade process where you will have mixed versions.
I wouldn't recommend running in mixed for an extended period of time. While technically it is fine. From an operational standpoint if there is issues you now have to take into account is it the version and drivers with that versions that's the issue. basically adds additional complexity when troubleshooting issues in the cluster.
When running mixed its recommended to not upgrade hardware or tools until all are at the same version.
Is it advisable to keep the the mismatch version in the cluster provided the vm hardware version stays as on the old ver5.1?
My recommendation is only during the upgrade process due the facts already explained on previous post.
If i can keep the ver5.1 and and 6 in the cluster ,Should I have to upgrade the vmtools whether VM resides on esxi5.1 or 6?
You can upgrade the VMware Tools to the latest, since newer VMware Tools supports run on old vSphere ESXi hosts. What you can't do is upgrade the virtual hardware for the lasted, otherwise you will be unable to vMotion the VM back to vSphere ESXi 5.1 hosts.
See more about VMware Tools compatibility: Is a VMware Tools Upgrade Required When Upgrading vSphere? - VMware vSphere Blog - VMware Blogs---
Senior Infrastructure Specialist
You can have mixed version of esxi in one cluster.But for better performance and troubleshooting use the same version of esxi