VMware provides several ways to upgrade ESX/ESXi hosts.

vSphere Update Manager
vSphere Update Manager is software for upgrading, migrating, updating, and patching clustered hosts, virtual machines, and guest operating systems. Update Manager orchestrates host and virtual machine upgrades. If your site uses vCenter Server, VMware recommends that you use Update Manager. For instructions about conducting an orchestrated host upgrade, see Using vSphere Update Manager to Perform Orchestrated Host Upgrades. For instructions about conducting an orchestrated virtual machine upgrade, see the Installing and Administering VMware vSphere Update Manager documentation.
Upgrade or migrate interactively using an ESXi installer ISO image on CD/DVD or USB flash drive
You can run the ESXi 5.5.x installer from a CD/DVD or USB flash drive to do an interactive upgrade or migration. This method is appropriate for deployments with a small number of hosts. The installer works the same as for a fresh installation, but if you select a target disk that already contains an ESX/ESXi 4.x, ESXi 5.0.x, ESXi 5.1.x, or ESXi 5.5.0 installation, the installer upgrades the host to 5.5.x, and gives you the option to migrate some existing host settings and configuration files, and preserve the existing VMFS datastore. See Upgrade or Migrate Hosts Interactively.
Perform a scripted upgrade

You can upgrade or migrate hosts from version 4.x ESXi and ESX, version 5.0.x ESXi, version 5.1.x ESXi, and version 5.5.0 ESXi to ESXi 5.5.x by invoking an update script, for an efficient, unattended upgrade. Scripted upgrades provide an efficient way to deploy multiple hosts. You can use a script to upgrade ESXi from a CD, DVD or USB flash drive, or by PXE-booting the installer. You can also call a script from an interactive installation. See Installing, Upgrading, or Migrating Hosts Using a Script.

vSphere Auto Deploy
Auto Deploy is a new feature in vSphere 5.x. After an ESXi 5.x host is deployed with Auto Deploy, you can use Auto Deploy to reprovision the host and reboot it with a new image profile that contains an ESXi upgrade or patch, a host configuration profile, and, optionally, third-party drivers or management agents provided by VMware partners. You can build custom images by using ESXi Image Builder CLI. See Using vSphere Auto Deploy to Reprovision Hosts.
You can use the esxcli command-line utility for ESXi to upgrade ESXi 5.0.x hosts or ESXi 5.1.x hosts to ESXi 5.5.x. You cannot use esxcli to upgrade ESX/ESXi 4.x hosts to ESXi 5.5.x. The esxcli command-line utility requires the vSphere CLI. See Upgrading Hosts by Using esxcli Commands.

The esxupdate and vihostupdate utilities are not supported for ESXi 5.x upgrades.

Table 1. ESXi 5.5.x Upgrade Methods
Upgrade Method Upgrade from ESX or ESXi 4.x to ESXi 5.5.x Upgrade from ESXi 5.0.x to ESXi 5.5.x Upgrade from ESXi 5.1.x to ESXi 5.5.x Upgrade from ESXi 5.5.0 to ESXi 5.5.x
vSphere Update Manager yes yes yes yes
Interactive upgrade from CD, DVD, or USB drive yes yes yes yes
Scripted upgrade yes yes yes yes
vSphere Auto Deploy no yes, if the ESXi 5.0.x host was deployed using Auto Deploy yes, if the ESXi 5.1.x host was deployed using Auto Deploy yes, if the ESXi 5.5.0 host was deployed using Auto Deploy
esxcli no yes yes yes