Replying to Car question

so my problems started about a week ago. after a very cold night my car wouldnt start. tried to jump the car and it didnt work. so i decided to take it to an auto parts store to be checked out. they said the bettery is good and they charged it right on up for me. i put the battery back in the car and the car started no problem. i probably started the car four five times till i tried to start it again and it didnt start. called my roommate to come give me a jump. well the jump worked and i drove home and let my car run for about a half hour. again the car started four five times and now this afternoon it wouldnt start again. the battery is back from febuary of '06 so it is about five years old. i live in northern minnesota so it gets quite cold every year. so I'm thinking either the battery needs to be replaced or something is wrong with my alternator. what are my chances a new battery will fix my problem?