Count your calories and make sure you get a little bit of each food group everyday. Protein should be 10-35% of your total calories. Fat = 20-35%. Calories 45-65%. Increase your calories a little each day, that might help gain a little. Look at a chart, you need to gain 5-20pounds, but i'm not sure, All i know is that someone who is much shorter than you (5inches shorter) who weighs 90 has to weigh 110lbs total. Even though the limit for healthy for a 5foot person is 97lbs, a doctor or nurse would tell them to reach 110. Gain muscle mass, YES!
You are at that age where boys are experiencing sudden growth spurts upward. Today you are 5 feet tall, tomorrow you wake up to find you are 5'5", then when you put on a few pounds, up you go again to 5'8". With each growth spurt you "lose" weight for your height. Don't sweat the small stuff. You certainly don't want to lose weight, so for now just eat healthy, frequent meals with fat, protein, variety and color. Enjoy yourself and don't worry so much about it. Concentrate on being healthy and forget the weight scale for now. Since muscle weighs more than fat, body building will help you to gain weight and keep your body fat down. Just get good correct advice on how to go about lifting weights and building yourself up. good luck