gibson for the story on this one. I am going to think that the '0' i ndicates the '1960 Classic model---'0' indicated 1960 on the original 1960 LEs Pauls and for the Reissue 1960's, also. Imho, the use of this scheme on the Classic series is misleading, but that is waht Gibson did, right? I have seen folks who knew no better think that they had a Reissue or even once an original 1960 LEs Paul because of that 0_xxxx number.
anyway, I think the '0' inidicates the 1960 Classic model, the '3' following the 5 indicates 2003. The 5 indicates that the numbering exceeded '9999'...so they fill the blank with the next largest digit. AT least, that is what would have happened with the original numbering system that used the first digit as the last digit of the year. Example.....
1960 original.....0_xxxx. When and if they exceeded 9999 for the serialization within that year, the number would read 01xxxx...becoming 6 digits rather than 5.
Gison will clue you in for sure on that guitar.