Make sure you call them drives- because they certainly are not disks anymore. Using NVMe M2 drives in your MacPro 5,1 can help speed it up considerably. And you can boot from NVMe drives with the latest EFI firmware which would have been installed if you upgraded to Mojave (also the last upgrade without hacks for the 5,1). I've purchased some PCIe carriers for M.2 drives and put them into my Mac. Somethings worked and some didn't. This post will take you thru what you can and can't do.
Your 5,1 has 4 slots. 2 are x12 lane PCI and 2 are x4 lane PCI. Normally you'll have a GFX card in one of the x12 - Slot 1. Below is a photo.

I purchased a x4 single carrier- it holds one M.2 drive. (StarTech or ST)
I also purchased a x16 quad carrier- it can hold four M.2 drives. (ASUS)
I also purchased a 1TB and a 512G M.2 drive to use.
For the ASUS- being x16 - each M2 is taking up 4 lanes. (4x4=16) and so it can carry the load of 4 drives.
The MacPro is over 10 years old, but it's x12 slots should be able to handle three M2 drives in the 4x card.
But it can't- it seems like the firmware isn't setup to do this.
Bottom line is that with just two M.2 drives in the ASUS - the card is not recognized in either of the x12 slots (Slot 1 or 2). I tried both. Putting one drive in and it's fine. By not recognized I mean the firmware EFI is not recognizing it - it's totally absent from OSX's view of the hardware.
Of course the StarTech x4 drive is fine in any of the slots. The x4 Slot is only physically wired up for x4 lanes- the slot is large enough to handle bigger PCI cards but the connections are not there to the mainboard.
But here is what you can do:

Mac loaded up with 4 cards (4th is a USB3 PCI card)

StarTech ~$15

ASUS ~$60
I migrated my boot disk over from a EVO 850 1TB SSD to the Samsung EVO 970 M.2 and the results are amazing. The MacPro is much snappier and I can feel the speed bump doing most things- about the same as going from spinning to SSD disks. If your MacPro has an empty slot or two this is very worthwhile investment to keep this amazing system going thru 2020.

SuperDuper doing a great job migrating my Boot disk over to the M.2 drive.
Your 5,1 has 4 slots. 2 are x12 lane PCI and 2 are x4 lane PCI. Normally you'll have a GFX card in one of the x12 - Slot 1. Below is a photo.

I purchased a x4 single carrier- it holds one M.2 drive. (StarTech or ST)
I also purchased a x16 quad carrier- it can hold four M.2 drives. (ASUS)
I also purchased a 1TB and a 512G M.2 drive to use.
For the ASUS- being x16 - each M2 is taking up 4 lanes. (4x4=16) and so it can carry the load of 4 drives.
The MacPro is over 10 years old, but it's x12 slots should be able to handle three M2 drives in the 4x card.
But it can't- it seems like the firmware isn't setup to do this.
Bottom line is that with just two M.2 drives in the ASUS - the card is not recognized in either of the x12 slots (Slot 1 or 2). I tried both. Putting one drive in and it's fine. By not recognized I mean the firmware EFI is not recognizing it - it's totally absent from OSX's view of the hardware.
Of course the StarTech x4 drive is fine in any of the slots. The x4 Slot is only physically wired up for x4 lanes- the slot is large enough to handle bigger PCI cards but the connections are not there to the mainboard.
But here is what you can do:
- Boot from M.2 drives on the carriers
- Mount M.2 drives using single carriers for as many free slots as you have
- Enjoy the enormous speed increase from SSD SATA to PCI NVMe (10x)

Mac loaded up with 4 cards (4th is a USB3 PCI card)

StarTech ~$15

ASUS ~$60
I migrated my boot disk over from a EVO 850 1TB SSD to the Samsung EVO 970 M.2 and the results are amazing. The MacPro is much snappier and I can feel the speed bump doing most things- about the same as going from spinning to SSD disks. If your MacPro has an empty slot or two this is very worthwhile investment to keep this amazing system going thru 2020.

SuperDuper doing a great job migrating my Boot disk over to the M.2 drive.