Simply not enough info to comment intelligently. Frame sizing numbers are all over the place. My 51cm LOOK has a shorter reach and head tube than my 48cm Colnago. If the frame is really too small, you'll need a 120mm or longer stem and probably a +6 angle to get the bars up to a decent height.
Height alone means little. I'm only 5'-6" but my leg length is as long as some people 4 inches taller. I used to buy 54 or 55cm traditional frames to fit my leg length, but the reach was always too long.