Where hunting deer with 5.56mm is legal, it will work just fine with the right cartridges, good marksmanship and the normally required knowledge of anatomy. The terminal ballistics are good with military loads at close enough range (pretty close) or some of the heavier commercial hunting bullets or even properly loaded match bullets (little longer range, especially with enough barrel/velocity). Larger calibers are fine, too, of course.
“...good marksmanship and the normally required knowledge of anatomy...”
Time was when Grandpop and Dad taught that to junior at a young age.