I have a lot of 5.56 ammo (including a lot from all those turrets I keep blowing up) but I cant find the gun that shoots it. Anyone know where to find one?

Assault rifle. Can find them all over.

Yes the assault rifle, you don't get them at low level but at medium one they are common, supermutants use them a lot.

Assault rifles are nice at full auto, for semi the combat rifle is better.