Dualcore 2.66gHz Mac Pro with the ATI 1900xt graphics card and 6GB of RAM.

I'd hate to spend $800 and realize it won't work completely. Thanks.

https://www.adobe.com/products/premiere/systemreqs/

yes, but you won't get hardware accelerated playback using the mercury PB engine....

It works completely on 2006 iMac an even H264 is completely workable, but as Steve said, you won't get CUDA acceleration.

Can I get that by upgrading my video card? Sorry for the n00b questions.

I am not a Mac guy so I don't know, but I didn't think all the Macs from 2006 were 64 bit. I would trust the other opinions over mine. Just make sure you are running a 64 bit operating system.

Can I get that by upgrading my video card?
No, i am afraid that wont do the trick.

From the FAQ:
...For example, the NVIDIA Quadro FX 4800 for Mac requires MacPro 3,1 or MacPro 4,1 (2008 or 2009) or later. MacPro 1,1 and MacPro 2,1 are not compatible.

To see what Mac Pro you have, click on the Apple icon in the upper left corner of your Mac Pro screen and chose About This Mac. The model identifier should be MacPro 3,1 or MacPro 4,1 (2008 or 2009) or later.

...I didn't think all the Macs from 2006 were 64 bit. I would trust the other opinions over mine. Just make sure you are running a 64 bit operating system.

It is likely that the OP's 2006 Mac Pro is still running a 32-bit operating system at present. Therefore, it cannot run CS5 at all unless the OP upgrades (updates) the OS to a 64-bit one. And CS5 requires MacOS 10.5.7 or higher just to even run at all. So, even if the 2006 Mac Pro is running a 64-bit OS, the OS that it is currently running is likely to be of an older version than the 10.5.7 required to run CS5 at all.

All of the Intel processors used in the Macs are 64-bit capable. Unfortunately, that 2006 Mac Pro is almost certainly of version 1.1, the very first released version of the Intel-powered line. Therefore, it cannot be upgraded to a video card that can use the GPU acceleration feature of MPE.