Is that card listed on the ESXi HCL (http://www.vmware.com/support)? If not you can check out some of the ESX "Whitebox" sites and see if anyone has listed it as working, but the best way is to get a card that's on the HCL.
Support Request #12150692803, regarding Storage connectivity issues on your ESXi 5.0 hosts. Based on our last communication, the LSI 1064E controller is not supported and is incompatible on ESXi 5.0 hosts.
