This is not an endorsement of shooting deer at 500 yards with anything, much less an SKS, but...
When I was a kid my Dad was employed on a huge Arizona cattle ranch part of which was adjacent to a small town. They had a problem with dogs from the town going stray, packing up and running cattle to death. Of course the owners would never believe that their sweet poochy had anything to do with any stock depredation so the policy became to just shoot the dogs. They would've preferred to shoot the dog owners, but that is illegal.
One day my Dad got a call that some dogs were running cows on the ranch and he headed out with his Model 94 Winchester carbine. A .30-30 with a short barrel, and iron sights.
After tear assing down a ranch road we found the dogs, my old man took a shot on a running German Shepard at (later paced out) 650 yards and dropped the bag bastard dead as Hell with one round through the chest.
Now the old man fully admitted that it was a pure luck shot,made by guessing a huge lead and hold over, but none the less it did drop a deer sized animal in one shot with a ballisticly similar round.
So in theory, an SKS could drop a deer at that range. Not reliably, not morally or responsibly and not too damn often, but it could happen.