I've been out for quite some time, but when I was in there was a minimum of 5'4" and no max that I was aware of.
I knew two Marines during my time, that were both taller than you are. If it's the same, and you can get in with your height (which I don't think is an issue), you'll find that some MOS's are not going to work.
For example, you need to fit into a cockpit to be a pilot, you need to fit into the tank to be on a tank crew, etc.
I think anything in the 03 field would be wide open, also Intel, Artillery, etc. They'll special order uniforms that fit you, but they won't order equipment to fit you. That should be a good rule of thumb.
But send an email to Larry Mullen and ask for the height/weight requirements.
JB