How big is this environment?
Please get a second opinion before acting but in that situation I would rebuild the vCenter. All of the VMs would still run without the vCenter. Having a distributed virtual switch in play would complicate that by requiring a network migration on standard virtual switches first. It can be a rough road to upgrade past 5.5. The biggest obstacle is the jump from 5.5 u3a t o 5.5 u3b which changes the underlying encryption from SSL to TLS. Either way, follow the VMware Update Sequence and update vCenter before ESXi.
5.0 Update Sequence
5.1 Update Sequence
5.5 Update Sequence
6.0 Update Sequence
6.5 Update Sequence
Whatever your starting point for the upgrade, click on the one above that matches. Note that if you just went straight for a fresh install of 6.5 that you would not need to worry about baby steps or some things not quite being the same because they were upgraded rather than freshly installed. If you were already on 6.0 then I would absolutely recommend just doing the upgrade because it already has the Platform Services Controller, but starting at 5.0 you will be changing the way SSO operates with the domain and so many other things that you may want to look into whether upgrading all the way from there is really the best path.
For example, I have seen a vSphere environment jump straight from 4.0 to 5.5 and almost nothing worked correctly. A more senior VMware admin looked at it and said that it was a huge mistake for them to try upgrading through that much of a jump rather than doing a clean install. I would really like to hear the input that others here would have on that.
