A little late but oh well. I've got a little experience of 5.56 on medium game from last hunting season, as always, your experience may vary. Tldr at the bottom
I got drawn for a November 2020 mule deer rifle hunt in New Mexico to the west of Albuquerque. A good buddy of mine had a little 400 acer ranch with a few water holes. There wasn't much else on the land, no good cover for deer, a few hills but mostly flat sagebrush. I got a few trail cams set just to see what was coming to the water, a few good bucks, does, and a lot of cows at times from the neighboring ranch. The best spot to watch the water hole was 175yrd away half way up a hill with my backup to a few trees. The trails into the water mostly wound around in a shallow arroyo, some 300-400 yrd out. My two choices for hunting rifle was a marlin 336 in 30-30 or a Dmr'ish AR I built in 223 Wylde. Due to covid I was having a hard time finding 5.56/223 hunting ammo or even 30-30 anywhere local. I figured my best option was to load us a few rounds of 5.56. My one source of luck was I had 4lb of Accurate 2230. Reloader buddy only had a few bullets available, 50grn Barnes Varmint Grenade, not going to work for deer, 55grn and 62grn fmj, not legal for hunting in NM, and 200rnd of 62grn Sierra GameKing, Figured that was my best option, Id heard good things about the game king line. I gave the buddy the rifle to build up a load for it, load came out to 1.2moa, good enough for hunting. The opening day came around, and saw nothing, day two was cool with low clouds. I got up early and was sitting in my lawn chair stand about 45M before dawn. About 20 minutes after I sat down I saw the gray flash of a deer in front, right out in the open, 107yrd away. I set the rifle up on an old fence post in front of me, the deer froze, put the crosshairs right behind the crook of the front leg, and gently squeezed the trigger. At this point I expected him to drop, but he turned and ran off over the hill. No problem, I'll probably find him piled up on the other side under a tree. I wait half hour, then I go looking, and I can't find anything. I walked back to where I shot him, and I can't find any blood. My mind was running through the normal stuff, did I miss, bad shot, the gun is zeroed good, good ammo, what happened? I started searching again, back over the hill, still looking. Can't find anything so I started all over again, this time I'm looking for the thickest brush I can, and I find him, still standing, 75yd away, standing slightly quartering away.. I fired two aimed rounds off the shoulder standing, first round hit too far back, liver shot. Round two I aimed higher he moved a little and a boiler room shot was not possible, round two hit in the top of the neck and he dropped like a sack of steel, stone dead by the time I walked up. It was odd, there was no blood anywhere, entirely holes where almost nonexistent, no exit holes. The moment I moved the head blood started pouring out of the mouth. Started gutting, guts were a bloody mess, the rear liver hit probably to blame there, I got lucky that the bullet didn't hit any guts. I started to pull the heart and lungs. The left lung was a mass of hemorrhage, but no holes, heart and other side looked OK. Single broken rib on the inside left side. Got him hung in a big tree and went to skinning, found the first bullet right under hide, dead center in the ribs. It hit one rib and stopped, broke the rib but did not penetrate further. The third round did perfect, high center neck, hit no bones, but sure shut off the lights. After I started looking into the GameKing line I found something out, in 22 cal they don't make a medium game bullet, it's all meant for Varmint, that's why the rapid expansion and no penetration. This was a bullet choice failure, nothing else, I chose the wrong option without doing the research. 5.56 definitely works on medium game in the hog and deer size. I've got a skull on the wall to prove it, but bullets matter much more than in a more traditional caliber. As to what works, not sure, my suspect list is Barnes tst, 75grn gold dot, and 77grn otp mabe, not sure on the last. I've got no other experience on 5.56 on game, ended up moving to Alaska and I won't carry 5.56 for much of anything up here. Too much for small game, much too little for the moose and caribou, never minding black and brown bears.
Tldr 5.55 needs the right bullet, under penetration is a problem, use true duty ammo at close range.
Left side where the first round hit, impact right next to the knife tip, third pic is of exit wound in the neck.
Recovered 62grn Sierra Gameking form under the left side hide after impacting the one rib.