That speed is determined by the strength of earth's gravity and by the size of the earth. When you are relatively "near" the earth (say within about 300 miles from the surface) and traveling horizontally, the earth's gravity bends your path in such a way that you drop about 16 feet down from your original path in a period of 1 second (This is true regardless of your horizontal speed). But it also happens that the surface of the earth, due to its curvature, drops about 16 feet in 5 miles. So if you are moving horizontally at 5 miles per second, then in 1 second you will drop 16 feet, but at the same time the earth's surface will "drop away" also by 16 feet (because of the 5 miles you traveled). The result is that you will go neither closer to nor farther from the earth in that one second. At the end of 1 second, you are still going horizontally at 5 miles per second, still at the same altitude, and the cycle repeats itself, all the way around the earth.

If you were to travel more slowly (say at 2 miles per second), then your altitude would drop more quickly than the earth's surface dropped away from you. You would find yourself getting closer to the earth with each passing second, eventually intersecting with it (ouch!).

If you were to travel more quickly (say at 6 miles per second), then the opposite would happen: In 1 second your path would bend by 16 feet, but the earth's surface would drop away by MORE than 16 feet. You would find yourself getting ever farther from the earth with each passing second. (This trend will stop after a while, and you'll reach a maximum altitude and then start falling closer again--unless your initial speed exceeds "escape velocity"; but that's another subject).

So, based on the strength of gravity, five miles per second (approximately) is the "perfect speed" to go in perfect circle whose radius is about the same as the earth's radius. If you want to orbit at much higher altitudes, the "perfect speed" is correspondingly smaller.*RickB