Hello Matthew,
Looks like you will have to upgrade to ~5.5 U2 and then to 6.5
The Interoperability Matrices are your friend here and will show you what can be upgraded to what for all the main VMware products:
ESXi
https://www.vmware.com/resources/compatibility/sim/interop_matrix.php#upgrade&solution=1
vCenter (Windows-based)
https://www.vmware.com/resources/compatibility/sim/interop_matrix.php#upgrade&solution=2
There may be other variables that need to be accounted for such as the DB-type of your vCenter and whether this can be upgraded:
Another thing to consider that will likely require upgrading is the VMFS datastore versions
https://kb.vmware.com/kb/1005325
Bob
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