Many players don't, and sometimes (unless you bought it from new) it can be hard to tell.
I was guessing that the '5' is either for Memphis.
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Les Paul Classic: This model features an ink stamped serial number with no “MADE IN USA” (just as we used on the original 1952-1960 Les Pauls).
Most will be 5 to 6 digits in length, but the earliest examples feature 4 digit serial numbers.