My thinking is that you could create a new folder in program files that you want the game to be installed in. You could then install your HDD and go to Disk Manager and mount the new drive onto the folder you want to install the game. Then install the game and tell it to install in the folder that you mounted your new HDD to. I don't know if Civ 5 is 32-bit or 64-bit, but if it a 32-bit program the Civ 5 install folder you created that the drive is mounted to should be created in Program Files (x86), otherwise it should be placed in Program Files, this only applies if you're running Windows 7 64-bit anyway. You could do the exact same thing with your C:\\Users folder so that personal files and other large files would be stored there if you want to. I haven't tried this myself but it should work, though there's a small chance windows may not allow you mount a drive to a subfolder in the Program Files folder for security reasons.
Keep in mind that's a little overkill and a far simpler option would be to just install the game straight onto the new drive without performing any of the drive mounting by using advanced install settings to specify an install location on the HDD. However, my personal preference is to have all my programs in program files, and the first way allows for certain files and folders to be stored to the HDD in a more transparent way.