If you have a earlier than MP51.0089.B00 BootROM version, these are the steps to upgrade your BootROM to have Mojave support:
- Disconnect any 4K or DP1.2 display. You can't update to MP51.0089.B00 with a 4K/DP1.2 screen connected to your Mac EFI GPU. It's a old bug that Apple corrected with MP6,1 and "forgot" to correct with the MP5,1. MP5,1 efiflasher don't support 4K screens or DP1.2, you can reconnect after you update your BootROM.
- Disable FileVault2 if enabled, since FV2 is not supported anymore with a Mac Pro 5,1 running Mojave.
- Install a Mac EFI64 GPU. Any original Apple card from 2008 to 2012 (HD 2600XT, 8800GT, Quadro FX 5600, GT120, HD 4870/5770/5870) or 3rd party Mac EFI cards like Sapphire HD 7950 Mac Edition, eVGA GTX 680 Mac Edition, NVIDIA Quadro 4000/K5000 or self-flashed/MVC flashed cards.
- If you use a SATA III PCIe card, remove your drive from the card and install into the Mac Pro SATA II ports, a lot of people report trouble doing the firmware upgrade with SATA III PCIe cards.
- If you ever downloaded any previous version of High Sierra, have it saved in any of Mac Pro external drives, you have to delete it/move to a offline disk and then restart your Mac. You need the current High Sierra 10.13.6 full installer from the Mac App Store, no previous version have the needed MP51.0089.B00 BootROM.
- This is the Apple Support page where you can get the link for the 10.13.6 Mac App Store Installer (you need this even if you already are on 10.13.6). see the image below. Note, if you never used Mac App Store before, you need to validate your account first and download a free app before trying to get High Sierra
Fabulous effort here, I commend you. Indeed I have an "earlier" boot rom (MP51.007F.B03) so this section applies. In Step 2 you say "...or self-flashed/MVC flashed cards." Assume you mean like the GTX980 I bought, flashed from MacVidCards? So no need to swap back to my Radeon 5870 then... I DO have what I think is a SATIII PCI card (they called it a SATA6G card, SeriTek 6G2+2) as my boot drive... if I do NOT boot from it, do I still need to pull it from the machine (I have a partition in my collection of drives that has a very clean 10.12.6, the latest nVidia drivers and a few drive utilities I'd use as a boot volume)?
Curious about re-downloading HS... I have an installer that I literally downloaded a month ago... how could it NOT have the firmware update? No biggee following your instructions, just curious. Oh, am running 10.12 6, no need to actually install HS/Mojave, correct?