1st: Why open a new thread exactly about the same issue of your previous thread?!?
2nd: there is no firmware updates for MacPro5,1 AFTER Mojave, once you have 144.0.0.0.0 installed, you are done.
3rd: Only High Sierra and Mojave full installers can update MacPro5,1 BootROM. The former up to MP51.0089.B00 and the latter from MP51.0089.B00 to 144.0.0.0.0. Catalina and newer does not have firmware updates for a MacPro5,1.
Please fully read this first post, you will probably find that you have one or more problems described into the various notes below. Mojave will only install if you have upgraded your BootROM to the current release and your Mac Pro have a Metal capable GPU*. If you are trying to install Mojave...
forums.macrumors.com
4th: Target Disk Mode will require a FW800 cable and is not the best way to test a disk. Anyway, you can try it.
5th: Internet Recovery is not available with a MacPro5,1, so, is useless to try anything related with a blank/defective disk, you need to create a createinstallmedia USB installer.
Run AHT/ASD and see if you have a harware defect somewhere.
AHT/ASD:
You need an Apple OEM GPU (HD 2600XT, 8800GT, Quadro FX 5600, GT120, HD 4870/5770/5870) to run AHT/ASD. AHT/ASD can be used with PC flashed GPUs, but will fail mid test with a sensor error when the GPU sensors are tested. Non flashed PC GPUs won't work at all. You need to boot completely vanilla, no OC, to use AHT/ASD.
You can get AHT links and instructions on how to install it on this GitHub article.
AHT, you need 022-4831-A.dmg:
Apple Hardware Test Download Links. Contribute to upekkha/AppleHardwareTest development by creating an account on GitHub.
github.com
The ASD version that you need is 3S149. The AHT instructions are valid for creating an ASD USB key and Apple provides an installation PDF with it.
ASD, you need 3S149:
As an information architect, these are a few tools, articles, and miscellanea that I find useful.
www.loremipsum.info
For people that have an early-2009 cross-flashed with MP5,1 firmware, you will need to run the MacPro5,1 versions of AHT (022-4831-A) and ASD (3S149).