My brother and I have been using the 5.56 for a number of years now. For us it has accounted for only about 15 deer. All have needed one and only oneshot. The farthest any have traveled was 50 yards or so which is in the same as with the other calibers we have used. Many were DRT. Both of us have been hunting deer for more than 45 years. As with any deer round, there are two very important issues.
First and most important is that you must place the round where it is supposed to be placed. If that means you need to pass on a shot because of distance, brush or position of the deer, pass on it. The second is closely tied to the first, use a bullet that is designed for deer sized game. In the past number of years, bullet companies have developed and produced bullets with the abillity to expand and give adaquate penetration. Do your research find well made bullet that is accurate in your particular AR. The 5.56 will do its job if you do yours.
As with anything, be sure that you do as much as possible to learn about deer hunting. From identifiying them, to tracking to habits, and evey facet of their life. Get out in the woods with an experienced hunter and learn everything you can. You owe this to the deer and to yourself. Stay proficient with your firearm.
I have been fortunate enough to have been able to hunt for over the past 50+ years. During that time, I have taken more deer then I remember and have helped track, find and process many more for the family. The size of the bullet has some consideration but when you have an adequate round, are confident and good enough with your firearm, and have the maturity and knowledge to where to place the bullet and when to shoot, your effort will be rewarded with some of the best food Mother Nature has to offer. It's not the arrow that kills the deer but the Indian. So far in every case where I have had to track a deer for a long distance, it had been shot with a larger caliber rifle. In every case, the shot was poorly placed. Use your 5.56 with confidence.