At this writing, Readers have not yet definitively reported on what might be keeping some MacPro 5,1 silver towers from updating their Firmware to the new version MP51.0083.B00 included with High Sierra. (Specifically, no one who was NOT able to update their firmware has reported a "Eureka, I found it!" moment where they were able to update after they "fixed" something.)
We have seen reports of Rotating and SSD Drives (in the regular Drive Bays) updating firmware properly, so drive type is (so far) NOT implicated. Rotating drives are NOT converted to APFS automatically in the .0 version.
• Candidates for precluding firmware upgrade still include unusual peripherals, and any PCIe cards that are not standard.
• Candidates include non-Mac-firmware graphics cards (without EFI firmware on board) until there is evidence that they are NOT to blame.
• Candidates also include non-standard Wi-Fi cards, added after the Mac shipped.
• There may be others I have not though of. Can you think of any that should be added to this list?