You can upgrade your ESXi 5.1 host to version 6 just using the Interactive Installer, take a look: Upgrade Hosts Interactively
Upgrade interactively by using an ESXiinstaller 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.
On the link above there is some prerequisites to check and remember that you will need a new license to assign to the ESXi version 6. And of course, is always recommended make backup of your VMs before upgrade.