I have read that you CAN fire .223 out of a gun chambered for 5.56 but you are not supposed to shoot 5.56 out of a gun chambered for .223.
It has to do with the leade of the barrel. Ill post this from another forum:
* The 5.56mm and .223 Rem chambers are nearly identical. The difference is in the "Leade". Leade is defined as the portion of the barrel directly in front of the chamber where the rifling has been conically removed to allow room for the seated bullet. It is also more commonly known as the throat. Leade in a .223 Rem chamber is usually .085". In a 5.56mm chamber the leade is typically .162", or almost twice as much as in the 223 Rem chamber.
* You can fire .223 Rem cartridges in 5.56mm chambers with this longer leade, but you will generally have a slight loss in accuracy and velocity over firing the .223 round in the chamber with the shorter leade it was designed for.
* Problems may occur when firing the higher-pressure 5.56mm cartridge in a .223 chamber with its much shorter leade. It is generally known that shortening the leade can dramatically increase chamber pressure. In some cases, this higher pressure could result in primer pocket gas leaks, blown cartridge case heads and gun functioning issues.
* The 5.56mm military cartridge fired in a .223 Rem chamber is considered by SAAMI (Small Arm and Ammunition Manufacturers Institute) to be an unsafe ammunition combination.