Tenzo,
You were driving on borrowed time with a 5-year old battery here in Chicago. Get a replacement. As for the alternator, that may be a problem as well, but in any event you need the battery first off. Most service places will do the electrical system check when you buy the battery from them. Otherwise, if you have a voltmeter, you can do a few simple measurements (car running, car not running) and determine if the alternator is putting out or not.
Good luck. (I change my battery before it gets to be 4 years old as preventive measure. This allows me to do it at my convenience and when they have a sale...)
Bob