  The existence of pentaquarks, namely baryonic states made up of four quarks
and one antiquark, became questionable, because the candidates, i.e. the
$\Theta^+$ peak, are seen in certain reactions, i.e. p+p collisions, but not in
others, i.e. $\ee$ annihilations. In this paper, we estimate the production of
$\Theta ^{+}(1540)$ and $\Xi^{--} (1860)$ in $\ee$ annihilations at different
energies using Fermi statistical model as originally proposed in its
microcanonical form. The results is compared with that from pp collisions at
SPS and RHIC energies. We find that, if pentaquark states exist, the production
is highly possible in $\ee$ annihilations. For example, at LEP energy
$\sqrt{s}$=91.2 GeV, both $\Theta ^{+}(1540)$ and $\Xi^{--} (1860)$ yield more
than in pp collisions at SPS and RHIC energy.
