PawPaw, folks have been shooting the 5.56 NATO round in 1000 yard matches since it was first allowed in competition back in 1971. While it's initial performance that far down range was dismal at best, later on with heavier bullets and faster twists, it did pretty good.
But it's never been the equal of the 7.62 NATO round at 1000. Which is why the US Army Rifle Team quit using it in long range matches a year or two ago and got the rules changed to allow the AR10 in 7.62 NATO be designated a "Service Rifle" for competition; they no longer had any good M14NM's to use. People shooting 7.62 NATO ammo in Garands and M1A's were shooting better scores that those using the 22 caliber round.
Never the less, it's fun to shoot those tiny bullets at things way far away. And some folks get really good at it.
US Navy Distinguished Marksman Badge 153
Former USA Palma Team Member
NRA High Power Long Range High Master
NRA Smallbore Prone Master