How to enable VT-x for Docker on MacPro 2008
The CPU in the Mac Pro 2008 does have VT-x support, so the CPU has the capability in itself.

However, you need to update the EFI firmware to actually enable the support so it can be used from macOS / OS X. You'll need to update to version 1.3.

You can find the download link here:

https://support.apple.com/kb/DL95?locale=en_US

You can find the official explanation from Apple here:

https://support.apple.com/en-us/HT203296

If you already have the EFI update installed, then VT-x should be enabled by default.

If it still isn't you can find the source code for a program on the link below that will both tell you the current state (enabled/disabled) for each CPU-code, and then turn on VT-x.

https://www.linux-kvm.org/page/Enable_VT-X_on_Mac_Pro_(Early_2008)

The program requires you to be running Linux on the Mac Pro. You could also run a virtual machine (although slowly without VT-x) in order to run the Linux program from there.

The last thing to try if you cannot get the official EFI updater to install the EFI update, is to flash the firmware manually by following the instructions on this link:

https://pubmem.wordpress.com/2011/04/09/flash-efi-firmware-update-manually-on-a-macbook-51/

However, this is very risky if you don't know what you're doing. You risk bricking the computer if you flash the wrong file.