If you’re running ESXi in standalone mode (that is, without using vCenter), you can apply patches online from VMWare directly.
Your ESXi server will need direct access to the Internet. First you must allow it to access the network by creating a firewall rule:
esxcli network firewall ruleset set -e true -r httpClient
You can then use the following command to download and install the patch:
esxcli software profile update -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-5.5.0-20150204001-standard
The image name (after the -p parameter) is used for selecting the patches you want to apply. You can find the list of patches at the excellent v-front.de website – https://esxi-patches.v-front.de/ which is also where I found these instructions.
Running a white box (generic PC) ESXi server is fraught with issues. I’m still working out how to upgrade my ESXi 5.1 server to 5.5 or 6.0, without losing the drivers for my Realtek network cards and SATA storage. I use network attached storage on a Qnap device for running VMs, but still use the internal SATA drives for image backups, logs, and other things, so I want to retain the ability to use those drives as vmfs storage.
More on my progress with that later.