Neither for your vCenter or ESXi you cant directy upgrade to 6.5 so a new/fresh installation might be a good idea compared to upgrading to 6.0 first with a inplace upgrade.
Note:
- vCenter on Windows is dead. VCSA is the new king
- No SSO anymore... its renamed to PSC and works "similar"
- New vCenter also supports running older ESXi version [1]
- Install a new VCSA 6.5 or 6.7 (if SnS allows the upgrade and your Backup/$OtherStuff supports 6.5/6.7)
- If you choose a new IP/Name you can run both in parallel and can tranfer the the settings from the old to the new vCenter manually
- If supportet by your hardware install fresh ESXi 6.5/7 on 1 or 2 Hosts
Well... now the problem starts
- Shutdown all the VMs on the last ESXi and perform an Upgrade to 6.0. Join the new vCenter and migrate the VMs to the other 2 Hosts and start them. Consider VMware Tools und vHW update later
If you dont upgrade and choose also fresh install you will lose the registration of all VMs. But ESX 5.0 is to old for managing by a 6.5 vCenter so you need to upgrade.
If all VMs are migrated you can reinstall this Host also.
[1] VMware Product Interoperability Matrices
Regards
Joerg