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Abstract Inspired by the fully heavy tetraquark states reported by the LHCb, ATLAS and CMS Collaborations, we perform a systematical 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 $$cccc\bar{b}$$ c c c c b ¯ and $$bbbb\bar{c}$$ b b b b c ¯ systems with $$J^P = 1/2^-$$ J P = 1 / 2 - and $$3/2^-$$ 3 / 2 - , $$cccb\bar{c}$$ c c c b c ¯ , $$bbbc\bar{b}$$ b b b c b ¯ , $$cccb\bar{b}$$ c c c b b ¯ and $$bbbc\bar{c}$$ b b b c c ¯ systems with $$J^P = 5/2^-$$ 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.