Looking for a vintage road bike, im about 5'7 so I figure my size would be from 52cm to maybe 56cm is that about right?

I start with stand over height. You want some room between the top bar and your jewels. You should be able to stand over the top bar and lift the front tire off the ground without injuring yourself. Different bike designs have different seat tube lengths with the same stand over height. I am 5'8 and have bikes from 51-54. There are some pretty good web sites on bike fitment, because the rest of the fitting process is more involved.

I reckon 54cm.

I don't think you'd be comfortable with anything bigger..

I am about 5' 7" and 54cm is the limit for me.

There are a lot of threads about fit, and opinions are all over the board. Height, body proportions, frame geometry, riding style and bike setup are all important and without knowing something about each it's pretty hard to generalize. That said, I'm about your size and a 54 is probably my "ideal" size for a road bike; nonetheless my most comfortable bike is a 56.

It totally depends on the length of your legs, arms etc. Long legs = taller frame, and vice versa. And don't forget that the top tube length is rather crucial, too. You can only compensate so much for wrong length without getting into trouble with the balance and weight distribution.

I've found that some of the free bike fit programs seem to give numbers that actually fit well with what already feels right. If I remember rightly, this https://www.competitivecyclist.com/za...der=M&units=cm was one of them. As my proportions are not absolutely average, the fact that it came very close to my own ideals speaks in favor of it.

Apart from that, this guy is an old sage https://www.peterwhitecycles.com/fitting.htm and I think his attitude is better, in fact, than slavishly following a formula.