The first thing you should do is measure your inseam. Here's how: Determine your proper frame size. You can choose to do the calculations on that page if you wish, but all you really need to know is your inseam size (leg insem, not pnats inseam). Once you know that, you'll be able to figure out which bikes will maybe fit, and which bikes won't. Then when you see ads for used bikes, you'll know if the bike is in the right size range for you.

I'm also 5'8", and I have a 32 inch inseam, which means I should be looking at bikes with a 31 inch or smaller standover height. I ride a 23" Motobecane, but could go down to a 21", according to that link I gave you. So I would say for me, the range I can ride is between 21" and 23". As long as you have 1-2 inches of gap between the top tube and you on standover, you'll be fine.

One more thing on size: Different bikes with the same nominal size will have diffferent standover heights, so you can't just assume that because a size-- say 21"-- is "your size" that all 21" bikes will be the same size. You will still need to check for fit. The value of knowing your size is that you can rule out all the bikes that are obviously too small or too big.

Also, different manufacturers measure their sizes differently. Some measure the frame from center of the crank to center of the top tube (c - c), and some measure from center of the crank to top of the seat tube (c - t). So when a bike is sized at say 21", you need to know what measurement method was used.

Finally, some vintage bikes will be sized in inches, and some in centimeters. You'll need to know your size in both inches and centimeters. The conversion rate is 2.54 centimeters per inch. You can also find metirc conversion calculators online.

Good luck!