  We search for strange pentaquark states that have been previously reported by
other experiments -- the $\Theta(1540)^+$, $\Xi_5(1860)^{--}$, and
$\Xi_5(1860)^0$ -- in 123 fb$^{-1}$ of data recorded with the BaBar detector at
the PEP-II $e^+e^-$ storage ring. We find no evidence for these states and set
95% confidence level upper limits on the number of $\Theta(1540)^+$ and
$\Xi_5(1860)^{--}$ pentaquarks produced per $e^+e^-$ annihilation event that
are about eight and four times lower than the rates measured for ordinary
baryons of similar mass.
