VMware provides several ways to upgrade ESXi 5.x hosts to ESXi 6.0 hosts.

vSphere Update Manager
vSphere Update Manager is software for upgrading, migrating, updating, and patching clustered hosts, virtual machines, and guest operating systems. vSphere Update Manager orchestrates host and virtual machine upgrades. If your site uses vCenter Server, VMware recommends that you use vSphere Update Manager. For instructions about performing an orchestrated host upgrade, see Using vSphere Update Manager to Perform Orchestrated Host Upgrades. For instructions about performing an orchestrated virtual machine upgrade, see the Installing and Administering VMware vSphere Update Manager documentation.
Upgrade interactively by using an ESXi installer ISO image on CD/DVD or USB flash drive
You can run the ESXi 6.0 installer from a CD/DVD or USB flash drive to do an interactive upgrade. 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 ESXi 5.0.x, ESXi 5.1.x, or ESXi 5.5.x installation, the installer upgrades the host to 6.0. The installer also gives you the option to migrate some existing host settings and configuration files and to preserve the existing VMFS datastore. See Upgrade Hosts Interactively.
Perform a scripted upgrade

You can upgrade hosts from ESXi 5.0.x, ESXi 5.1.x, and ESXi 5.5.x to ESXi 6.0 by running 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 specifying a preboot execution environment (PXE) for the installer. You can also call a script from an interactive installation. See Installing or Upgrading Hosts by Using a Script.

vSphere Auto Deploy
After an ESXi 5.x host is deployed with vSphere Auto Deploy, you can use vSphere Auto Deploy to reprovision the host and reboot it with a new image profile. This profile contains an ESXi upgrade or patch, a host configuration profile, and optionally, third-party drivers or management agents that are provided by VMware partners. You can build custom images by using vSphere ESXi Image Builder CLI. See Using vSphere Auto Deploy to Reprovision Hosts.
esxcli
You can use the esxcli command-line utility for ESXi to upgrade ESXi 5.0.x hosts, ESXi 5.1.x hosts, or ESXi 5.5.x hosts to ESXi 6.0 hosts.

The esxupdate and vihostupdate utilities are not supported for ESXi 6.0 upgrades.

Table 1. ESXi6.0 Upgrade Methods
Upgrade Method Upgrade from ESXi 5.0.x to ESXi 6.0 Upgrade from ESXi 5.1.x to ESXi 6.0 Upgrade from ESXi 5.5.x to ESXi 6.0
vSphere Update Manager Yes Yes Yes
Interactive upgrade from CD, DVD, or USB drive Yes Yes Yes
Scripted upgrade Yes Yes Yes
vSphere Auto Deploy Yes, if the ESXi 5.0.x host was deployed by using vSphere Auto Deploy Yes, if the ESXi 5.1.x host was deployed by using vSphere Auto Deploy Yes, if the ESXi 5.5.x host was deployed by using vSphere Auto Deploy
esxcli command-line utility Yes Yes Yes