5'11" isn't actually that bad for 13hh, you look a little silly but they can carry you fine - Shay-la had two 13hh ponies she broke in and she's around the 5'10"/5'11" mark. I also had to do some riding on them for her when she broke her leg, and I was around 170lbs then and 5'6"? Ponies are tougher critters, but as a "regular" riding horse, I wouldn't do it. If you're just looking to tune her up for someone smaller, she can probably handle it.
Pics of Shay-la on Max, a 13hh pony:
Me standing next to him (I'm 5'6")
And me riding Max: