Morning Gary
Welcome to the Forum
A bit confused about which Model is your car an M5 550dx Touring (lucky boy if it is) or one of the other models with M-tech accessories like say a 530d M-tech.
As far as Battery is concerned the main Battery should be either 92ah or 105ah AGM (under the floor in the boot) and will need registering to your chassis to ensure correct charging. Just to confuse the innocent your car may have an additional battery under the Bonnet for the Aux heating and suspension which could be either AGM or Lithium the AGM should be 60ah (I think) not sure about the Lithium, again I believe these batteries need registering to the chassis.
Hope this helps not hinders
Dave