@WrightBro No matter what you do, please be mindful of the VMware Update Sequence. For example, always upgrade vCenter before ESXi. You can get lucky and deviate from this sequence sometimes and not have issues, but other times you will create critical errors. I have confirmed personally that trying to update ESXi before vCenter can and will break everything. This can be explained because if there is a jump in encryption (or other protocol adjustment) that vCenter needs to be the first to know about it or else it won't be able to communicate with the host once ESXi gets updated.
I would definitely seek a second opinion, but if crossing past the 5.5-u3B divide, I strongly recommend building a new vCenter. vSphere 6.0 comes out with the Platform Services Controller and other fundamental changes to the architecture. But the most awkward speedbump/landmine along the way is that with 5.5 update 3B you jump from SSL to TLS to avoid the POODLE vulnerability. If you are in an environment where everything is hardened to the point of being nearly unusable, then you might not be able even to upgrade from 5.5 3A to 3B. That is as far as the ESXi versions go for 5.5, and from there are many incremental patches requiring the VMware Update Manager (VUM), but vCenter goes up to 5.5 u3E. Finally with 3E VMware's KB documentation says that they resolved many problems with upgrading that were unresolvable with 5.5 u3D, but I'm not quite convinced. The whole 5th generation of vSphere is something that I would recommend avoiding traces of by having a clean install of vSphere 6x. Not to mention that with 6.5 the new standard is to use the VCSA. I would go for a straight installation of that. Upgrading does not always give you the same capacities but only brings you close to what a clean installation feels like. I can provide some documentation on that if you prefer.
If you have fast equipment these upgrades will happen in minutes. If you have slow equipment a vCenter upgrade can take 5 hours and an ESXi upgrade can take an hour. On solid state ESXi can upgrade in a couple minutes. Once the upgrade is successfully complete, and the system shows evidence of stability, you can migrate some VMs onto it and go ahead and start upgrading the next one. There's no point in adding artificial time gaps between upgrades unless that's just how small your update windows is.
