Interesting question, LOL. A bullet traveling at 3,600 miles an hour, must be made out of titanium or some such material. Depleted uranium might work, but that would be extremely expensive. The fastest I know of is a 40 grain 243 that could reach 4,000 fps, but I am sure it would burn up before it reaches one mile or 5,200 fps.
Because of air friction, all bullets will slow down at some point in their travel they will go from supersonic to subsonic during their travel so any measurement of 5,200 fps would only be at the tip of the barrel. Along with the pull of gravity downward it might be a physical impossibility to get a load that would give you the results you are looking for.
Good luck, you could try it in outer space where gravity and air friction would not apply. Stay safe and take plenty of oxygen with for your tests.
Jim