I could not find the updates first and then I was wondering how to apply them.
Here’s the way I used. I followed the guide from vland found here: http://www.vladan.fr/esxi-free-how-to-upgrade-to-esxi-5-1/
Login to the ESXi 5.1 host and check under Configuration/Software/Security Profile/Services/Properties if the SSH service is running. If not start it and consider if you let it run automatically. At least until you have applied all updates.
Next shutdown the running VMs.
Next download the updates from here: http://www.vmware.com/patchmgr/findPatch.portal
I downloaded 3 zip files from there: ESXi510-201210001.zip, ESXi510-201212001.zip and ESXi510-201303001.zip
Upload them with the vSphere client to the host. There are other ways to upload files but the vSphere client is OK.
Now use a SSH client and connect to the ESXi host with your credentials. I sue putty from here: http://www.chiark.greenend.org.uk/~sgtatham/putty/
Next run this command in the SSH session:
esxcli software vib install -d /vmfs/volumes/[DATASTORE]/[PATCH_FILE].zip
You can use TAB for completion of directory and filename 😉
Run the command and check the output:
It should show at the beginning that the update was successful and the box needs to be restarted. Restart and after the restart repeat for the other patches.
That should it be.
Thanks to vland!!!