Find yourself a teen beginner ballet class. It is not too late for recreational ballet. It is too late for a career as a ballet dancer. Aside from having to have a ballet body which is much more than just being thin and the right height, you must be in the 2% of the population born with ballet feet, turnout and a few other things that you cannot change no matter how much you train. Most people are clueless as to what it take to become a professional ballet dancer. You start at age 7 or 8 at a world class ballet academy that will only train girls who have the correct bone structure. At your age, dancers are taking 30 hours of technique classes a week and even more in the summer and have done so for years. They dorm at their ballet academies and are home schooled or take academics as arranged by their academy. Training is complete at age 16 when they apprentice with a professional ballet company and if lucky are asked to join as corps de ballet 6 months later. Most ballet academies will not even look at girls that have had no training who are older than 10 or 11 even if they have the right body and facility for ballet. However, there have been some rare exceptions of dancers at the ripe old age of 12 or 13 that have convinced a ballet academy to train them. These few dancers were so exceptional, that despite starting that late, they have become successful. Even of the dancers who started at the right age with the right body and facility, and have studied in world class academies like the School of American Ballet, many of the girls don't make the professional ranks. There are so few jobs and many well trained dancers. I have never ever heard of any professional female ballet dancer starting later than 13 and as I said that too is very, very rare.
All this being said, who says you have to get paid to enjoy dance. Dance for the the Joy of Dance. Dancer's careers are very short and the pay isn't great. The sacrifice on you life and body is very great for very little return. Dance can always be part of your life.
*Although Soibhan is correct when it come to men in ballet (many start at age 14 and 15) it is too late for a girl to go professional. That is because different things are required of a female dancer like dancing en pointe for one thing. There is also a lot more trained female ballet dancers to choose from so only the cream of the crop gets work.
My daughter is a professional dancer.
I worked for NYCB (New York City Ballet)