Migrating from vSphere 5.5 to another datacenter 6.5
If you don’t worry about powering off the VMs, you can copy them over SSH. It's exactly what I did to migrate my production a while ago and the migration was succusfully completed. Also there was a good article about production migration:
https://www.starwindsoftware.com/blog/virtual-workload-migration-with-vmware.
Regarding VMs – there are no restrictions in moving to 6.5 – here’s the compatibility link:
https://pubs.vmware.com/vsphere-65/index.jsp?topic=%2Fcom.vmware.vsphere.vm_admin.doc%2FGUID-64D4B1C9-CD5D-4C68-8B50-585F6A87EBA0.html