Re: battery or alternator?
I personally wouldn't attempt to jump it anymore. Take your battery out of the car and have it checked. It may have to be charged first if infact a defective alternator run it down, but doubtful.
5 years on a battery, I would replace it anyway. I just replaced my original in my '04 and it wasn't giving me any trouble, but I didn't want to find out somewhere on the road when it decided to go south.
Just a note whether some agree or not: If you have a dead battery in a car, when possible, always use a battery charger to bring it back up. An alternator is designed to maintain battery voltage, not bring a battery back from the dead. A dead battery puts an extra heavy load on the alternator that could shorten the life of it. Now if you need a jump in the middle of the night in a dark alley to get home, that is another thing.
James