mass - Precision of Coulomb's law

Up to which precision has the coulomb law proven to be true? I.e. if you have two electrons in a vacuum chamber, 5 meters appart, have the third order terms been ruled out? Are there any theoretical limits to measure the precision ( Planck's constant?). Obviously there are practical limitations ( imperfect vacuum, cosmic rays, vacuum fluctuation). Still, does anyone know what was the smallest amount ever correctly predicted by that law?

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Edit : Summary

On the high end of the energy spectrum a precision of 10^-16 has been shown ( 42 years ago )

For electron point charges at large distances the law might brake down due to practical reasons.

For moving particles QED gives a correction to the law: http://arxiv.org/abs/1111.2303

Answer

Quoting from my copy of the 2nd edition of Jackson's book on Classical Electrodynamics, section 1.2:

Assume that the force varies as $1/r^{2+\epsilon}$ and quote a value or limit for $\epsilon$. [...] The original experiment with concentric spheres by Cavendish in 1772 gave an upper limit on $\epsilon$ of $\left| \epsilon \right| \le 0.02$.

followed a bit later by

Williams, Fakker, and Hill [... gave] a limit of $\epsilon \le (2.7 \pm 3.1) \times 10^{-16}$.

That book was first published in 1975, so presumably there has been some progress in the mean time.