I have seen a number of HP 5334A with corroded traces due to leakage from the Ni-Cd memory backup battery. Because of this, I open and inspect my unit every 6 months for signs of failing battery. In the last month, I notice error 52 and 51.X when I power up or recall settings. I suspect the battery has failed, when I measured it out-of-circuit, the nominal 3.6V is now at 0V. When I charged it, the battery no longer accept charge.
Luckily, I was able to catch it before it leaked. While the NOS of the original battery is still available, I decided to switch over to NiMH. The Varta Mempac has an exact voltage and pin layout, and it fixed both error messages.
When the unit is on, the battery is charged at a constant 7mA through R50. The battery has a 150 mAh capacity, so the current is well below the 0.1C threshold for the NiMH battery, and the constant charge should not create heat or overcharge issue.
So far so good, you may want to keep any eye on the battery on your 5334A, especially if you start getting these error messages.