Start making a createinstallmedia of Sierra/ElCapitan with another Mac, boot from the createinstallmedia USB installer with your Mac Pro and HD 5770, nuke your disk, partition/format it, finally do the macOS install to the disk.
Even with your VEGA GPU without pre-boot configuration support (aka BootScreens/BootPicker), your Mac Pro will boot from the createinstallmedia USB installer when you only have the installer and a new/erased disk on your Mac Pro.
I upgraded my two macs with a security updates from Apple. Both updates killed my internet on both machines.
Story: On Wednesday 19th July 2023, I accepted Apple's security update on my 5,1 Mac Pro running Monterey.
Then, the internet became patchy on the machine.
I felt this was a security concern, so I accepted the security update on the OS Ventura running my MacBook 15.4" Pro circa late 2017, and that update completely and straight away, killed the internet on the MacBook Pro. That was running Ventura 13.3.1.
I spent considerable time trying to get the MacBook Pro's internet working again. Eventually I took it to Apple where they put the OS on the machine. In their Genius Bar environment, the recovery mode saw the Apple server. The machine now works, now running Ventura 13.5.
As said, the Mac Pro also lost its internet (although Safari would work under recovery mode, a software install from Apple's server would not work, the call being not being able to see the server (being Apple's).
A re-install is difficult on a Mac Pro because I run a 580 X metal card in order to run Monterey etc. So there seems no way that I can quickly re-install Monterey from a USB stick, due to the black screen (I presume as the graphic drivers cannot be loaded early on) and hence I cannot choose which drive to install Monterey, even if there is only one formatted and empty drive in the 5,1 machine.
Is there a way to install OS without replacing the GPU card with Apple's original 5770? I have an almost new Eizo monitor, and I am unsure if the original GPU will connect to it. Plus there is the time factor ... but now I am desperate and so, I am prepared for the long haul.
I do have an early non metal OS on a hard drive which I can pop in after replacing the GPU, and start from there ... I presume the internet will work, but I am unsure of the steps forward from there ... Help would be appreciated.
If I can recover the machine, I will use super duper etc to make an identical internal drive with Monterey on it ...
This is annoying a I did have a Sierra OS in partition of 4TB back up drive, but when I tried to reboot from that Sierra drive, the system would not load. I suspect due to some corruption in that 4TB back drive, or maybe it was due to it being partitioned.
Can someone point me to the steps required to start from scratch on the 5,1 to get back to Monterey?
I'd like to mention too, that the Genius at the Applestore, pointed me to a page for getting the OS to upgrade the 5,1, and he said if that doesn't work, then bring it in. But now Apple have informed me that the machine is not supported and if I want help, to go to a non Apple owned repairer. They do not acknowledge any fault with their security update ... which soon changed. The Applestore knew of the problem, and my internet provider said that many Apple users had lost their internet capacity while the Windows machines in the same environments had no issues. So it was definitely an Apple update problem - no doubt due to the M processor commitment.