This is the fastest method of updating ESXi 5.0 to 5.1 without using vSphere Update Manager.

Note that the commands below work for vanilla ESXi 5.0 installation, if you have added any custom drivers, DO NOT continue or risk losing connectivity to your ESXi server.

1. Enter Maintenance mode.

2. SSH into ESXi host server.

3. Allow HTTP downloads in Firewall rules:

esxcli network firewall ruleset set -e true -r httpClient

4. View available profiles:

esxcli software sources profile list -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml

5. Choose the latest standard Image Profile version available, f.e.:

esxcli software profile install -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-5.1.0-20121201001s-standard --ok-to-remove

6. After the update successfully completes, reboot the ESXi host server.