Get the battery charged, tested and replaced if needed.

Also keep in mind these cars do not really have a Voltage regulator per say.

The battery needs to be registered and programmed as the DME controls the charging Voltage and a good battery and proper programming is key.

Not a problem if the same Amp Hour battery used.

Do you have an AGM battery in the vehicle?? Not sure I would use one of these in one of these vehicles.

Also have you checked the charging Voltage??

I think you can bring up the Hidden OBC menu and display the charging Voltage on the dash?? Search here or on the M5 forum for Hidden OBC Menu.

Proper charging Voltage should be around 13.5 Volts.

A poor mans load tester to to turn the headlights on with the vehicle off, leave the lights on for 2 minutes and the battery Voltage should not drop below 12.2 Volts on a half way decent battery.

And yes, when the battery or charging system goes haywire in these cars, your dash turns into a Christmas Tree!