If it meets the Adobe Premiere Pro CS5: System Requirements you can install it. Using it is another matter, because it is way underpowered for editing.
Chances are it will not work, because you need a DEDICATED SATA drive next to the OS disk.
Mac OSX v10.5.8 meets the minimum system requirements, but the Core Duo processor does not. If you meant to type Core 2 Duo, then you're OK. The Core Duo is not a 64-bit processor. The Core 2 Duo is.