51cm I would think? Although they seem to come up small, they are a gents frame. I am 5'9 and typically ride a 54.cm road bike, so I'd probably need the 57cm, thus the 51cm sounds right for someone half a foot shorter (I also have quite long arms and legs). You may need to add narrower bars, a shorter stem and of course a women's saddle
Best is to go sit on one and ride around the store if you can
However, according to the website, Birmingham has none in the store and only a few sizes for home delivery - they have been selling like hotcakes