  We analyze the possibility of the existence of a fully exotic pentaquark
state $udsc\bar{b}$, which is made from the five different flavors
participarting in the strong interactions. We investigate the coupled channel
effects of the $B^{(*)} \Xi_c-B^{(*)} \Xi_c^\prime$ system through $t$-channel
vector meson exchange to search for such states. A $B \Xi_c$ and a $B
\Xi_c^\prime$ bound state are found to have binding energies of about
$10-30$~MeV with $B_s\Lambda_c$ and $B_c\Lambda$ being the possible decay
channels. Similarly, a bound state is formed in the $B^* \Xi_c$ and $B^*
\Xi_c^\prime$ channels, respectively. These states could be searched for
through the $pp\to B_c\Lambda X$ or $pp\to B_s^{(*)}\Lambda_c X$ processes by
the LHCb collaboration.
