Road bike (commuter) frame size problem
I am roughly your size (same inseam 5'8&quot;) and 52cm for a &quot;standard&quot; diamond frame bike would be too small for me. With a long enough stem I could get the bars in roughly the right place, but it they would likely be too low without some serious bogdery with stem riser extensions. But if you're young and flexible enough to deal with the low bar position it might work for you.
However, 52cm doesn't really tell us enough about the exact frame geometry to know whether this bike is appropriate or not. It's close enough that you can likely ride it safely if not as comfortably as possible. A picture or link to the exact bike would help a lot in answering this question.
A bike only becomes &quot;unsafe&quot; when you can't get the proper seat height w/o having enough seat post in the frame seat tube. There are markings on the seat post ( generally around 4 inches). Or you can't pedal the bike w/o your knees hitting the handlebars ( generally this is when standing to pedal).
Beyond the basics bike sizing is mostly about getting the compromise of comfort and efficiency in fit that works for you. If you were a pro bike racer, 52cm might be ideal. For the average rider, you can likely make the bike &quot;work&quot;, but you'd be more comfortable on a slightly bigger bike ( either 54 or 56cm depending on exact geometry.)