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.