  This paper presents the results of inclusive searches for the strange
pentaquark states $\Theta^+(1540)$, $\Xi_5^{--}(1860)$ and $\Xi_5(1860)^{0}$ as
well as the anti-charm pentaquark state $\Theta_c(3099)^{0}$ in a dataset of
123.4 fb$^{-1}$ collected on and 40$ $MeV below the $\Upsilon(4S)$ resonance by
the BABAR detector at the $e^+e^-$ PEPII storage rings. No evidence for the
pentaquark states is found and upper limits on the rate of $\Theta^+(1540)$ and
$\Xi_5^{--}(1860)$ production in $e^+e^-$ annihilation are obtained.
