rita

5 kg (about 11 pounds) is totally doable in a month but with your statistics ( 5'3" and about 112 pounds) I think losing that much may be a bit more difficult since you are not even overweight to start with. Maybe you should only try to lose te 2-3 kg you have gained and no more.
The answer to weight loss? Diet, Diet Diet (about 80 percent of success)
Add some exercise (cardio and weight training)
For your diet you should consume about 1100 calories per day, eating a lot of protein, whole grains, vegetables and fruit. Skip (or limit greatly) sugar, cookies, candy. No white bread, pasta, white rice. For dessert have a piece of sweet juicy fruit or a small scoop of ice cream or frozen yogurt. Lots of big salads with tons of vegetables and 2-3 tablespoons of low calorie dressing. A protein rich food such as eggs, fish, lean meat, non-fat dairy or beans at every meal or snack.
Drink lots of water (or other low calories liquid).
Don't skip breakfast.
Eat at least 2 servings of non or low fat dairy per day (it actually helps your body to get rid of fat).
Cardio: 30-45 minutes, 5 -6 days per week. It could be running, walking at an incline (the higher the better), elliptical trainer, jumping rope, biking, etc.,
Weight training: 30 minutes, 2-3 days per week.
Do not eat less than 1100 calories per day.
You should lose the extra 2-3 kg in a month with no problem.