,
As per the document you attached, page 6 shows that the maximum version supported is 5.5 which is extremely old and of course, it reached End of Life. Now, what you checked is that the CPU model is supported, but the hardware itself it is not as per the VMware HCL.
If you make the upgrade, the server will not be supported as it is not in the HCL, it may work, but you face an issue related to ESXi itself, you will not have a 2nd option.