  Inspired by the fully heavy tetraquark states reported by the LHCb, ATLAS and
CMS Collaborations, we perform a systemical investigation of the low-lying
fully heavy pentaquark systems composed of charm and bottom quarks (anti-quark)
in the chiral quark model. With the help of the channel-coupling, we obtain
several fully heavy pentaquark candidates, which are $cccc\bar{b}$ and
$bbbb\bar{c}$ systems with $J^P = 1/2^-$ and $3/2^-$, $cccb\bar{c}$,
$bbbc\bar{b}$, $cccb\bar{b}$ and $bbbc\bar{c}$ systems with $J^P = 5/2^-$. The
binding energies of these states are all below 10 MeV and the root mean square
(RMS) are around 1.8 fm, which indicates that these states are likely to be
molecular states. These predicted exotic states may provide new ideas for
experimental searches and we expect more experimental and theoretical
researches to study and understand the fully heavy states in future.
