  We present the first study of $N_f=2+1+1+1$ lattice QCD with domain-wall
quarks. The $(b, c, s)$ quarks are physical, while the $(u, d)$ quarks are
heavier than their physical masses, with the pion mass $ \sim 700 $ MeV. The
gauge ensemble is generated by hybrid Monte Carlo simulation with the Wilson
gauge action for the gluons, and the optimal domain-wall fermion action for the
quarks. Using point-to-point quark propagators, we measure the time-correlation
functions of quark-antiquark meson interpolators with quark contents $\bar b
b$, $\bar b c$, $\bar b s$, and $ \bar c c$, and obtain the masses of the
low-lying mesons. They are in good agreement with the experimental values, plus
some predictions which have not been observed in experiments. Moreover, we also
determine the masses of $(b, c, s)$ quarks.
