  We investigate the mass spectra of exotic hadrons known as pentaquarks. We
extend a simple phenomenological model based on the G\"ursey-Radicati mass
formula for hadrons to include both charmed and bottom baryons as well as to be
able to predict masses of pentaquark states including both charm and bottom
quark-antiquark pairs. In particular, we perform numerical fits of this model,
which includes seven free parameters, to masses of 21 baryons. We find that the
model can be well fitted to the experimental values of the baryon masses and
observe that the predicted value of about 4400 MeV for the mass of the
pentaquark $P_c(4380)^+$ lies within the experimental range reported by the
LHCb experiment. In addition, the predicted value of about 4500 MeV for the
mass of the pentaquark $P_c(4450)^+$ is close to the experimental value.
Finally, in the future, other predicted values for masses of additional
pentaquarks could be shown to agree with upcoming experimental results.
