To upgrade your ESX 5.5 server to 5.5 Update 3b, you will need to do the following:
1) Shutdown all running VMs
2) Put ESX in maintenance mode
> vim-cmd /hostsvc/maintenance_mode_enter
3) Enable the outbound HTTP client through the ESX firewall
> esxcli network firewall ruleset set -e true -r httpClient
4) Perform the upgrade to 5.5 Update 3b. As always you can get information about this update or other updates on the VMWare knowledge base here and here
> esxcli software profile update -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-5.5.0-20151204001-standard
5) Reboot the ESX Server
6) List available updates that came out after the Update3b. You want the standard one and it can take FOREVER for it to complete, say more than 5-10 minutes with no feedback. You may see versions that include an "s" at the end of the filename, these profiles only contain security patches, not other bug fixes. These security only versions would be for those organizations that are restricted by their change control board from patching anything but security fixes.
> esxcli software sources profile list -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml | grep ESXi-5.5 | grep standard | grep 2016
7) You will see from this list that there is another update, as of today. It is called ESXi-5.5.0-20160104001-standard. If you wanted more information about this update, you can go to the VMWare Knowledge base and search on "vmware esxi-5.5, patch ESXi-5.5.0-20160104001"
8) Perform this update as well
> esxcli software profile update -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-5.5.0-20160104001-standard
9) Reboot the ESX Server
7) Exit maintenance mode:
> vim-cmd /hostsvc/maintenance_mode_exit
