These vintage Mac Pro desktops only officially support up to macOS Lion. Bad Apple! Fortunately there’s a very slick workaround:
The easiest approach for a clean install is to put the boot HD in a USB dock, plug that in to a working Mac running current macOS, format it with Disk Utility (GUID partition scheme), and use the createpikeinstallmedia script to put the installer directly on the drive. Swap it back into the Mac Pro, power up, and let the installer run. Note that 12GB RAM or more is required. As we had a few 4GB DDR2 Registered DIMMs lying around this was not a problem.
We picked up a vintage 2006 Mac Pro with dual 3GHz dual core Xeons and 7600GT video card for $25. macOS thought that there’s only 8MB video RAM (there’s really 256MB) so we swapped in a (circa 2011) Gigabyte Radeon 6670 that was lying around. Swapping in quadcore Xeons would be interesting but hardly required. Fun project.