You should get the measurements of the 51cm and compare. Seat tube shouldn't be a big deal, as pushing up your seat post about an inch more shouldn't be a big deal (maybe), but if you're already running a 120-110mm stem on your current 53-54cm bike, and the 51cm is hypothetically 2 cm less on the top tube, then you're going to have to use a really long stem, and/or more saddle to bar drop. But also note that seat tube angle steepens as the sizes go smaller on many bikes. The steeper (closer to 90) the seat tube angle, the more you have to set back your saddle for proper fit, which increases the distance from the saddle to the handlebars. So, even if the bike has a smaller top tube, the steeper seat tube angle can kinda make up for it.
btw, I'm 5'7", and I ride a 50cm, and it fits me very well. Then again, I'm asian and have short limbs.