I recently updated an ESXi 5.5 host to 6. This is a remote machine so didnt have access to load the ISO. This is how i did it via SSH and ESXCLI.
Running through the ESXi update:
Shut down all running VM’s
Put ESXi host into maintenance mode
Allow httpClient access out through the firewall.
esxcli network firewall ruleset set -e true -r httpClient
Run the following command to download and install the update. Make sure you use “update” here DO NOT use “install” as it may overwrite drivers that you need.
esxcli software profile update -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-6.0.0-20150404001-standard
Once that is complete, go ahead and reboot the host
After your host has rebooted, take it out of Maintenance mode
That should be it.