I have found a possible solution that was inspired by your problem. I have a Core i5-650 system with a H55 chipset and a 3ware 9650SE-2LP card and I'm now copying data to the disk on the controller.
I installed the driver twice. I use vCLI on Windows and did the following:
0. put the server in Maintenance Mode !
1. download the 5.0u1 driver from here: http://www.lsi.com/downloads/Public/SATA/SATA%20Common%20Files/esxi5u1_driver_LSI_3ware_96xx.zip
2. extract the "LSI_2.27.08.036vm50-offline_bundle-637081.zip" from it to a temporary directory (for instance C:\temp)
3. with the use of WinSCP or an alternative, connect to the ESXi server and copy the offline bundle to the root (should be the default path)
4. open vCLI (or install it first) and use the following command: C:\Program Files (x86)\VMware\VMware vSphere CLI> esxcli --server <server-IP> software vib install -d /LSI_2.27.08.036vm50-offline_bundle-637081.zip (don't forget to change <server IP>)
5. it should prompt you for the user name and password:
Enter username: root
Enter password:
6. then you'll need to wait a while, until you get the following:
Installation Result
Message: The update completed successfully, but the system needs to be rebooted for the changes to be effective.
Reboot Required: true
VIBs Installed: LSI_bootbank_scsi-3w-9xxx_2.27.08.036-1OEM.500.0.0.472560
VIBs Removed:
VIBs Skipped:
7. reboot the server
8. check that the controller is indeed installed (I found it in Configuration --> Advanced Settings --> Configure passthrough...)
Now here is what I did to actually make it WORK: repeat all the steps from above ! Also copying the driver to the root, as it will have been deleted when installed. After the reboot I found the controller in the "Storage Adapters" and then I could use the "Add Storage..." under "Storage" to add the "Local AMCC Disk" and I am now able to use it !
Hope it helps !