This would mean two upgrade of your VMware v Center Server, and two upgrade of your ESXi hosts.
I have written a number of guides on how to upgrade ESXi using VMware Update Manager: How to Upgrade ESXi 5.5 to 6.5 Note: ESXi 5.5 does not have a direct upgrade to ESXi 6.7.
It is important to check this guide for every component of your environment such as: You will need to verify the versions of any component that touches your VMware v Sphere environment.
Do not proceed with any portion of your v Sphere upgrade before doing so, or you may end up in an unsupported configuration.
Though the terms may be used interchangeably, the VMware Interoperability Matrix shows you interoperability between VMware products components.
Be sure to check out this detailed guide on how to update v Center Server to get comfortable with the process before you do it.
When it comes to updating ESXi, v Sphere Update Manager is hands down the easiest way to accomplish this.
It is a powerful tool that is very easy to use, and has been around for quite some time.
First, I accessed the VMware Interoperability Matrix and clicked on Upgrade Path.
Then I selected the component I wanted to upgrade, and accessed the results.