If it is marked 5.56 then it will shoot .223 just fine, interchangeably. If it is marked .223, it might have some ejection problems with 5.56 ammo, due to the cartridge being just lightly thicker, the dimensions are so very close to the same, that chambering a 5.56 in a .223 shouldn't be a problem, but could cause performance issues.
.223 specific AR barrels are pretty few and far between though... usually only for match or long distance type uses.