  Inspired by the observation of a resonant state $X(6600)$ of fully charm
tetraquark by the CMS experiment of LHCb Collaboration in double $J/\psi $
decay channel, we perform a systematical study of all configurations of fully
heavy pentaquarks $P_{Q_{1}Q_{2}Q_{3}Q_{{4}}\bar{Q_{5}}}$ ($Q_{i}=c,b$%,
$i=1,2,3,4,5$) in their ground states in unified framework of MIT bag model.
The color-spin wavefunctions of pentaquarks, classified via Young tableau and
presented in terms of the Young-Yamanouchi bases, are used to compute masses
and magnetic moments of fully heavy pentaquarks via numerical variational
method, predicting a set of masses ranging from $8.229$ GeV for the
$P_{cccc\bar{c}}$ to $24.770$ GeV for the $P_{bbbb\bar{b}}$. Combining with
computed masses of fully heavy mesons and baryons, we find that masses of fully
heavy hadrons(mesons, baryons, tetraquarks and pentaquarks) with identical
flavor rise almost linearly with the number of valence quarks in hadrons, being
consistent with the heavy quark symmetry in the heavy-quark limit.
