I don't know a lot about Nutanix, so I can't tell if there are additional options or restrictions in regard of the storage, but besides this it's important to know
- what's the version of ESXi and vCenter in the old and the new Cluster (I see 5.1 mentionend but I hope that's not the currently used version)?
- do you stay on the Essentials Plus license or do the new hosts come with new licenses?
In general Essentials Plus does not cover Storage vMotion, however it's usually still possible to migrate online with the option "Change both compute resource and storage". It may take some time as vRAM and disk space of the VM need to be transferred via the network, but should be doable with 10 Gb. Alternatively offline storage (and host) migration with the VM powered down is another option.
You usually don't need to get special temp licenses as an newly installed ESXi hosts operates in trial mode for 60 days (up to version 8, at least). The same applies to vcenter if you do a fresh install or upgrade to a higher release version (e.g. from 7 to 8).
But it all depends on the versions used and their interoperability...
Regards,
Carl