I believe I picked COR_H version due to having Firmware SKU = Corporate H displayed when running my dumped firmware through ME Analyzer as explained in this post:
Also note that my machine was Prodesk 600 G4 mini, not G5 so there are probably some additional differences to be considered in your case.
I also think that my BIOS had settings for Data Recovery set to something other than Automatic, but I’m not 100% sure on that.
In any case it does appear you managed to load a new firmware but failed to boot due to some other issue. Search online for HP Prodesk 600 G5 SFF Service Manual - see if beeps are explained there.
Or perhaps @lfb6 is onto something here and HP changed BIOS anti tampering protections in G5+ variants in which case I’m not sure how to proceed at this time.