Let's suppose we put 5 electrons on a perfectly conducting (no resistance at all) sphere.
There's no equilibrium configuration with 5 (though there is with 2, 3, 4 or 6). So will they keep moving on the sphere for ever ?
The answer seems to be that they end up in a non-symmetrical unstable equilibrium with three electrons equispaced on a great circle that we can call the "equator" and the other two at the poles.
This is what is observed in a pentacoordinate compound which is one with a central atom and five other groups (called "ligands") attached to the central atom. All the ligands are assumed to be identical.