How long should a battery last?
 

I had to jump my 540 today. I can't remember when I changed the battery but I think it was at least 4, maybe 5, years ago. I assume it's just an old battery but how do I know it's not the alternator?

Check what the voltage is at the battery when the engine is running at >2k RPM.
Should be above 12.5 volts all the way up the ~14.3.
Use a volt meter or read it in the cluster.
My battery lasted 8 years. The battery in my wife's 01 Volvo is original and still working fine....knock on wood.

The average lifespan for a BMW battery is about 4-5 years. If your battery is still original, I would play it safe & replace it. These have a nasty habit of being fine one day, and then the next day one of the cells will intermittently short out and cause a no-start. I've seen it too many times....You can check the age of the battery by checking the production date on the negative post; it will have the week & year of production(26/01, 26th week of 2001). To check the charging system, just put a voltmeter between the jumper lug on top of the driver's valve cover & the ground lug on the passenger shock tower. Check it with the car running. It should be around 13.7 to 14.2 volts. Anything lower or higher could show a faulty voltage regulator...

Some things you replace on a schedule; others you replace when their time is up:
- DIY how to test a BMW E39 battery & alternator