BMW 525i 2000-2003 has a battery in a trunk on a right side, to change battery ,you should leave your engine running & replace with the other as quick as you can, when you take the battery off ,the car wont go off & you wont need to reset your devices or enter any codes, and you wont make any changes to your central locking system or engine immobilizer.
On 2005 the battery is in trunk on the right hand side
Under hte rear seat on pass side
Battery is located under the rear seat. grab the corner and lift up. You'll need to enter the radio code for the radio to work as well as set time/date.