How long would it take an out of shape person to prepare for a 5k? ?

I really wanna run a 5k because it's a great cause and it's great for your health. The only thing is I'm pathetically out of shape. I am 20 yrs old, female, 5'6 and 155lbs. I work out occasionally but I have always had bad lungs cuz I was raised in a cigarette smoky house. Right now I can run 5mins straight on a treadmill at 6mph and 3 incline. after that I have to stop an walk. How long do u think it would take me to be ready for a 5k if I work out 3x a week. I'm in college so I don't have much more time to work out than that.