  In this paper I present an (\in, =)-sentence, AC**, with only 5 quantifiers,
that logically implies the axiom of choice, AC. Furthermore, using a weak
fragment of ZF set theory, I prove that AC implies AC**.
  Up to now 6 quantifiers were the minimum and 3 quantifiers don't suffice
since all 3-quantifier (\in, =)-sentences are decided in a weak fragment of ZF
set theory. Thus the gap is reduced to the undecided case of a 4 quantifier
sentence ZF-equivalent to AC.
