What is the minimum virtual machine compatibility setting required for a virtual machine to run on a vSphere 5.5 host?

ESXi 5.1 and later is a valid but more restrictive compatibility setting - it is not the minimum level that vSphere 5.5 supports.

ESXi 3.0 and later does not correspond to any defined VM hardware version in the vSphere product line; the earliest supported level maps to ESXi 3.5.

ESXi 4.1 and later corresponds to hardware version 7, which is a higher minimum than what vSphere 5.5 actually requires.

VMware vSphere 5.5 hosts can run virtual machines configured with hardware version 4 or higher, and hardware version 4 maps to the 'ESXi 3.5 and later' compatibility setting. This backward compatibility allows organizations to host legacy VMs on modern infrastructure without requiring a VM hardware version upgrade.