RRA's generally use the Wylde chamber, which should be fine with 5.56.  5.56 should really not be used in a .223-chambered rifle (most match/varmint barrels).

Also, note that the stampings on the lower receiver have absolutely NOTHING to do with the actual chambering of the rifle.  All BM lowers are marked "5.56/.223", but obviously you could be using a 6.8 SPC, .50 Beowulf, or even a .221 Ghengis upper.  It's all about the barrel, and you can't even trust those markings from many of the manufacturers.  A quick example.

Brand     Chamber*   Marking
============================
Colt      5.56       5.56
BM        5.56       5.56
Oly       5.56**     5.56
Armalite  5.56        -
RRA       Wylde       -
DPMS      5.56       223
ASA       223         -
Hesse/VA  223         -

*Chamber found on a typical 16" standard or M4 barrel.

**Note: older barrels were .223, but still marked 5.56.

Keep in mind this chart is for typical barrels; most manufacturers offer other barrels with different chamberings, and they often aren't marked properly.

-Troy