Apple Mac Pro "Quad Core"

No, you can't.

The Firmware would not run, the error-correcting code RAM would not work, the drives would not work.

DE7EASED:

"just to be clear this is the first Intel-based tower Mac, the Mac Pro "Quad Core" 2.66 that's powered by two 2.66 GHz dual core Intel Xeon 5150 processors"

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Understood.

All is Designed as One Device:

All hardware is built into the Mac to operate as one device. On much older Macs, however, you could always add RAM to possible levels. But, RAM is not a processor. The LogicBoard may corrode, which would be a health hazard. So, all being said, just don't fiddle with it.

DE7EASED Said:

"Oh I'm aware of that fact, that was unrelated, I'm just wondering because I can't find it not apples website"

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Blow it Off:

And you wont find it on Apple's Web site. So, blow it off, and don't proceed with this.

This site has a lot of usable ideas about how you CAN upgrade your classic Mac Pro:

https://blog.greggant.com/posts/2018/05/07/definitive-mac-pro-upgrade-guide.html#cpu21

It includes a note that the heatsink compound on the original Mac Pro pre-2008 models may be toxic.

DE7EASED:

"Apple Mac Pro 'Quad Core'" Yooo ,Could you put two i5's in a 2007 intel xeon Mac Pro????"

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Using Two Processors:

Never use a pair of processors; the heat will fluctuate and the device with inevitably fail.

DE7EASED:

"do you know the highest OS it could run?"

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Advancing th macOS:

That would make no difference. It is the model that would permit it to increase.