The fifth string peg is at the fifth fret because the string diameter pretty much has to match the first string, which is just about as thin as strings get. The fifth is tuned five semitones higher than the first, so in order to keep the string from breaking when it is tuned that high it must be shorter by that interval. This also allows the tensions to match, which affects tone and playability. Some British banjos from earlier times have the fifth peg on the peghead, but the fifth string _nut_ is at the fifth fret, the string enters a tube at that spot, and emerges at the peghead. Thus, the effective string length is the same as in a conventional five-string neck.

Thanks to Sean Barry for the above information.