Stair-climbing will be perfect for you. If you have a staircase run up and down it for 30 mins a day for those 5 months and you will really rev up your calorie expending. Do intense stretching before and after.
I will recommend exercising in a REALLY proper way which does not tire you up :)
With total honesty, running/jogging is by far the best thing you can do for your body by way of exercise. The running will burn major calories, so i think you will be surprised by how your muscles will tone up, and appear leaner. The weights are good, just be careful not to work out so much that it increases your appetite. I do cardio 5 days a week, after my weight training, and i do three days of running and two days of walking. The walking seems to help me with my lungs on the run days which is good. Hope this helps.