Hello. That's strange. You shouldn't have to mess with the boot rom at all, regular product code should handle rom updates for you. What software did you try and load via xmodem? You might try E.07.40 from the website, it should do a rom update for you.
Sounds like you've already tried an xmodem download, but perhaps the version of software you tried to download was too new (or large) for the rom you are currently running. From rom:
=> sp 115200 (optional, also change your terminal baud and reconnect)
=> do (send E.07.40 via xmodem)
=> jp 1
Then you from there load E.10.74, which should do another rom upate.
Code for 5300:
https://h10145.www1.hpe.com/Downloads/SoftwareReleases.aspx?ProductNumber=J4819A&lang=en&cc=us&prodSeriesId=5354494