To be clear, you have an old 5.1 environment with an old vCenter/Hosts/storage configuration. You want to move to a new 5.5 vCenter/Hosts and Storage configuration?
Yes, moving a 5.1 vCenter/Hosts/storage configuration environment to a 5.5 vCenter/Hosts/storage configuration environment.
I did some research and looks like one way to do this is to connect the storage environments together via fiber, mesh the zones and vmotion the VM's. My only issue here is the storage devices are made by different vendors so I may have to cold migrate.
I've done this before with a data center migration going from old to new. Lets call it old site A and new site B. They were on a flat layer 2 network so it was fairly straight forward. Here is what we did:
1) On the new SAN in Site B, present some NFS storage over the network to the hosts in Site A and Site B.
2) Configure specific hosts in Site A to have a "migration network" port group on a standard vSwitch which is an empty port group.
3) When ready to migrate a VM, storage vMotion it to the NFS datastore rather than the existing VMFS data store it lived on.
4) Once migrated, arrange downtime on the server and shut it down.
5) Once shutdown, note the network label and change it to the migration network label.
6) Remove the VM from Site A vCenter Inventory.
7) Add the VM into Site B vCenter Inventory, targeting the NFS datastore and the VM .vmx location. Change the network label back to equivalent network port group configured in Site B.
8) Boot the server on a Site B host on the NFS data store.
9) Check the VM boots correctly. If asked "moved or copied", select "moved". Upgrade the VMware Tools and shutdown.
10) Upgrade the virtual hardware.
11) Boot the server up for final time, confirm services.
12) Storage vMotion the VM back to Fiber Channel VMFS datastores in Site B.
This is a cut down version of the plan obviously but might give you an idea. This was from versions 5.1 to 5.5. I assume if you were taking advantage of vSphere 6 you could potentially harness long distance vMotion?
It did involve some downtime per VM, but a very short amount as the process becomes familiar. Probably better/quicker than a cold migration.
It was a fairly low cost solution in place for the organization at the time and we successfully migrated well over 500 VM's using this method.