Possible, perhaps. But it would require a LOT of exercise. I don't know your stats, but the heavier you are, the easier it would be for you to lose weight faster. However, if you are only overweight, and not obese, it would be quite difficult. Whatever you do, though, don't try to lose weight fast by cutting your calories extremely low! Unless you are very short/petite, I'd say you shouldn't ever go below 1,500 calories in your diet (and 1,800 would probably be even better). Less than that will probably cause your metabolism to shut down!
If you absolutely must lose weight this fast, then you should supplement a moderate diet with lots of exercise. Of course, you will probably have to work your intensity and duration of exercise up as you get in better shape (also, please check with your doctor about any exercise program, especially if you are overweight or have a medical history). Elliptical machines can burn a very high number of calories quickly, as can scuba diving, running, and other activities. Please be careful not to overexert yourself at first. It is easy to overdo it the first workout (pretty much because your legs tend to go numb and you don't notice how very much work they are doing). If you do too much all at once, you will feel it the next day! As you have 5 months (20 weeks), you should make a workout schedule that gradually gets longer and harder. For example, week one: 4 days per week 45 minutes walking, week two: 5 days per week 45 minutes walking/elliptical, week three: 5 days per week 1 hour elliptical/jogging, etc. That may be slow for you, or fast depending on your cardiovascular health. Just be careful and stay in touch with how your body feels. If your workout makes you hurt, you are pushing too hard. If you can easily sing while you exercise (after the first couple weeks), you may be going a little too easy.