You're about my size. Unless you have short arms, I think you may be too big for that frame. Standover may fit you, but on a sloped top tube frame, standover isn't an issue.

You can put the saddle where it needs to be, but at your height and inseam, you'd better make sure you aren't curled up over that top tube. Simply adding a longer stem is not generally a fix.

In my opinion, you'd be better on a 54 classic, and with that sloping top tube, a 52 would be fine. On a 50cm frame, you'd better test ride and then see if a stem change would work without going overboard.