Always a good idea to back-up the EPROMs of dated test equipment – rarely they fail, but very tough to fix, at least, if it is a less-popular unit. The 5372A is definitely less popular. Let’s make at least the EPROM images publicly available, I hope HP doesn’t mind!
There are 8 EPROMs: 4 pcs 128Kx8 HP p/n 1818-4060, and 4 pcs 512Kx8 HP p/n 1818-3825 (equivalent 27C512).
These are the hp serials and denominators of the EPROMS: