BMXes are mainly ridden out of saddle, so size isn't that important. but it's probably on the small side.
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A "real" BMX has 20" wheels, very small changes in frame size, and is almost always ridden standing up. That last bit makes them fairly unsensitive to rider's size.
Of course they can there are different sized BMX bikes. Of course there is a limit on how tall they can be. But I've seen people probably about 6'5 ride a BMX bike and they were real good.