According to Scott Duff's "The M1 Garand Serial Numbers and Data Sheets", HRA serial number 5565806 has been observed with barrel date 11 54 and HRA serial number 5567997 has been observed with barrel date 12 54.
While Garand receivers were not necessarily assembled into full rifles in sequential order, they usually were. The serial number you have was most likely manufactured in Nov or Dec or 1954. If it wasn't, it should have been built 1955 at the latest.
It is definitely C&R for CA to other states, and C&R for interstate sale (no FFL required for FTF).