  Motivated by questions in number theory, Myerson asked how small the sum of 5
complex nth roots of unity can be. We obtain a uniform bound of O(n^{-4/3}) by
perturbing the vertices of a regular pentagon, improving to O(n^{-7/3})
infinitely often.
  The corresponding configurations were suggested by examining exact minimum
values computed for n <= 221000. These minima can be explained at least in part
by selection of the best example from multiple families of competing
configurations related to close rational approximations.
