In addition to checking the VMware Compatibility Guide and VMware Product Interoperability Matrix that André mentioned, here are some things to consider:
1) ESXi 3.5.0 64607 is the GA build, which is not compatible with vCenter 5.1.
2) vCenter Server 5.0 is compatible with ESXi 3.5 U5 (build 207095)
3) ESXi 3.5 hosts are not upgradable to ESXi 5 directly - you would have to go to ESXi 4 first and then do a second upgrade to ESXi 5.
4) Need to verify if your old hardware and new hardware can exist in the same cluster with EVC enabled.
What kind of storage do you have and how many VMs (or how much data) do you have?