A rifle with a .223 chamber isn't built to handle 5.56 pressures. Regular use of 5.56 ammo can damage your rifle.
If it were marked "5.56 NATO" you'd be hunky dory to shoot either or through it.
Sgt. of Marines, 5th Award Expert Rifle, 237/250
1st Award Expert Pistol, 382/400
D Co, 4th CEB, Engineers UP!! OEF 21JUN-20SEP2011