What height is best for a cyclist?

There is no particular advantage for any height in cycling. Pros come in all sizes and all can do well. As far as frame size, I think your talking road bike, a ballpark size would be about 52-54cm. Start there and see how they fit. I'm 5-8 and ride a 52cm, but it always depend on the bike's design.

Any good bike shop will help you with the correct size of frame, handlebar reach etc., some have a jig set-up which they can adjust to your leg/torso/arm length to obtain the precise measurements, which are really crucial to getting the maximum benefit from the amount of effort expended, and equally important, for preventing injury.

At 5'9", your own height will not really have any bearing

on how your cycling would be affected, it is more about muscle type, power to weight ratio and the training method you adopt.

17-18" MTB frame or a 54cm road frame should be close if the rest of your dimensions are roughly average. However, as Intrepid says, its best to get measured and fitted, especially if you're intending to ride a lot or compete.

In case you were asking about professional cyclists, the prototypical seems to be 5'7* to 5'9" and 120-140 pounds. The elite climbers tend to be a little smaller, and there have been some very successful riders who were much larger, like Miguel Indurain.

Some think that Taylor Phinney (6'4") may just trash those stereotypes in a few years.

MR got the right idea, between 52-54, also it depends on if you have long legs/short torso or visa versa. Go to a specialty cycling store and have them to fit you a the proper frame for your height. This will help too if you do long distance. Sometimes you'll need some adjustment to your handlebars, seat too, to reduce back pain. Go to the pros.

Saves you time and prevent injuries.

Any size that you get on this board is just a starting point. Just like shoes, a certain size from one manufacturer may fit you and that same size from another manufacturer may not. Go to your local bike shop and let them fit you correctly. There is much more to it than just your height and leg length. Learn what a properly fitted bike feels like. Then you can make apples-to-apples comparisons with other bike shops. Test ride as many bikes as you can. One of them will fit you better than the others and you'll be able to tell that very quickly. Buy that bike regardless of brand name. It's the one you will use and enjoy the most.

HTH

there is no specfic height for cycling, as long as you have a suitable height of the bicycle and also know how to cycle.That the important thing.... :)

5'7