Shut down all running instances and put your host in maintenance mode. Your host must have SSH enabled.
1) Download the upgrade from VMWare and copy to ESXi host
2) Get the name or code for this update
3) Perform the update
1) At this time, the most recent version is VMware-ESXi-5.1.0-799733-depot.zip. If updated, you should be looking for "Download VMware ESXi 5.1 Installable" That is something like Home -> All Downloads -> VMware vSphere -> VMware ESXi 5.1 Installable. It's not all that easy to find. You need a login at VMware. When the file is downloaded, copy the file to somewhere on the host. Somewhere you can find.
2) You need the name or id of this particularly update. I'm not sure why that is, but you need it.
Change the location for the update file so it fits your location, and run the script. The result will be something like: ESXi-5.1.0-799733-standard or slightly different. This is the name/code for this specific update. Perhaps there really is no reason for all this. If you take a look at the file name (VMware-ESXi-5.1.0-799733-depot.zip) the code you need is right here (in the square brackets): VMware-[ESXi-5.1.0-799733]-depot.zip. It will properly work also.
3) Ready for the actual update.
If update file is located on datastor DS1, in a subdirectory called 'update' and code for this update is: ESXi-5.1.0-799733-standard, then something like this should be okay:
This may take some time, especially if you are running ESXi from a USB stick. Then the result is finally coming, it will be something like:
Message: The update completed successfully, but the system needs to be rebooted for the changes to be effective.
Reboot Required: true
Plus a lot of nonsense. Your host is now updated to 5.1. Please reboot the host.
First time connecting with the vSphere client, the client will need to be updated to version 5.1. As the host is now running version 5.1, VMware tools installed on all your VM's is also outdated (running version 5) For MS based VM's this should not be a major problem - they tend to run the update themself (mostly) For some reason, some MS machines will also need to be re-activated after the update. You must do this manually. For LINUX machines, you need to go over the VMware tools installation manually for each box.
Added 24/12 2013.
You can update the 5.1 host with the same method from patch 1 and up.
|ESXi510-201310001||5.1.0 Patch 6||2013-10-17||1312873|
|ESXi510-201307001||5.1.0 Patch 5||2013-07-25||1157734|
|ESXi510-201305001||5.1.0 Patch 4||2013-05-22||1117900|
|VMware ESXi 5.1 Update 1||5.1.0 U1||2013-04-25||1065491|
|ESXi510-201303001||5.1.0 Patch 3||2013-03-07||1021289|
|ESXi510-201212001||5.1.0 Patch 2||2012-12-20||914609|
|ESXi510-201210001||5.1.0 Patch 1||2012-10-24||838463|
|VMware ESXi 5.1||5.1.0||2012-09-11||799733|
Updating from ESXi 5.1 (1312873) to 5.5
I haven’t been able to find the 5.1-5-5 update from Vmware, but if your box is have access to the internet, you can do an online update.
Andreas Peetz at VMware Front Experience have made a very nice tutorial about both the online and offline update. Especially note the part about downloading the off-line update bundle (You can reset the firewall from the vSphere client when done. Configuration -> Security Profile -> Firewall -> Properties).