It can't run because your Mac Pro only has a 32-bit EFI. This is not an excuse for Apple for not making it work; I'm just noting the actual technical reasoning.
However, the simple workaround (if you have a Yosemite-compatible video card) that doesn't involve a Hackintosh-level install is to use a modified boot.efi file that thunks EFI64 calls from the 64-bit OS X kernel to the EFI32 firmware of your Pro. Look at the first post of this thread
and navigate to the section quoted below.
Another simplified installation approach is to use a second Yosemite-supported Mac and install Yosemite to the 2006/2007 Mac Pro's drive. This may be done either by attaching the 2006/2007 Mac Pro's drive as an external drive by placing the 2006/2007 Mac Pro in target disk mode or otherwise mounting the 2006/2007 Mac Pro's drive to a Yosemite-supported Mac. Then, after installation, copy Pike's EFI32 boot.efi to that drive's
/usr/standalone/i386 and /System/Library/CoreServices/ directories overwriting the stock Apple EFI64 boot.efi and repair permissions. That drive should now be bootable on a 2006/2007 Mac Pro
I'm typing this from my Mac Pro 1,1 (with an ATI Radeon HD 4870). I used a different Mac (recent Mac Mini) to install Yosemite to a drive, copied the updated boot.efi file, installed the drive into my Pro, and I've been good to go ever since.