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After the vCenter Server (described in the previous post) and the VUM part (this could a simple upgrade, by keeping the existing DB, or a re-install), you can go through the ESXi part.
A re-install from scratch could be simple, but you may loose some information (unless you use Host Profiles). For more information see upgrading to ESXi 5 vs doing a Fresh Install. Note that if you need 3rd part drivers, you may have to build your how ISO version (see: how to add ESXi custom drivers to the installation ISO).
But if you already start from a recent version of ESXi you can simple use VUM and keep all your hosts configurations.
First step is import the latest ESXi ISO in the VUM repository:
Now you can create an VUM upgrade baseline:
And apply it to your hosts:
Finally a scan and a remediate operation will upgrade your hosts.
Note that host will be booted first with the ESXi installer, will apply all the upgrade procedures and than will reboot again the host. The whole process may need around 20 minutes.
Finally remember to use VUM for a patch scan, and of course a remediation (considering that there are some patch that must be applied).