I'm a 2nd year PTA student who starts her final rounds of clincal rotations tomorrow morning. I stand 5'3 and, in my limited experience, I have found things difficult at times because I'm short and light. But I am still learning, and in general, my height has not kept me from excelling. There have been times when walking patients who tower a foot over me and weigh more than 100 pounds more than I do that I've realized I couldn't control as well as I'd like to if they were to fall, but part of my curriculum has been learning how to best position myself for a mechanical advantage in transferring, walking, or otherwise manipulating patients despite my stature or theirs. I may have a more difficult time than a taller, broader person picking up on techniques that best suit me, but it is possible, and it seems that it comes with experience.
One of my professors, a PT who has been practicing for almost 30 years, is shorter than me by at least two inches. She has demonstrated 1:1 transfers with larger, heavier people that have the rest of us in awe. She admits that being short has its disadvantages, but she has proven that it's only a matter of using proper body mechanics and figuring out how to make the situation work for her, whether it requires climbing onto a plinth, standing on a 6 inch step, making use of a lower mat table, or getting creative with patient positioning.
Being 5 feet tall is not a game ender. If you're passionate about PT, it will not hold you back.
As a side note, I would encourage you to consider job shadowing PTs and/or PTAs to get a first hand idea of what the job requires. A job shadow/observation would also be a great opportunity for having others weigh in on any concerns you may have. Great luck to you and keep us informed on what you decide to do!