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.
LCpl Williams, Evan T. USMC-R, 02-08-2010 ~
D Co, 4th CEB, Engineers UP!! OEF 21JUN-20SEP2011
REV. 19:11 And I saw heaven opened, and behold a white horse; and he that sat upon him was called Faithful and True, and in righteousness he doth judge and make war.