Bob Hewey and Tom DeLorey responded to Mark Borckardt's earlier question on the earliest appearance of a five-pointed star on any U.S. Federal regular-issue coin.
I expected someone to mention the Barber coins. The 1792 half disme is sort of a gray area, as some call it a pattern and others a regular issue. I personally agree that it is a regular issue, but it wasn't produced at the physical Mint building.
The Starred Reverse cent is a great choice and one that I had managed to overlook as my initial recollection was that they were six pointed stars. Reexamination shows that they are indeed five pointed stars. Thanks to Bob Hewey for his observations.