  We present the charged-particle pseudorapidity density in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02\,\mathrm{Te\kern-.25exV}$ in centrality classes
measured by ALICE. The measurement covers a wide pseudorapidity range from
$-3.5$ to $5$, which is sufficient for reliable estimates of the total number
of charged particles produced in the collisions. For the most central (0-5%)
collisions we find $21\,400\pm 1\,300$ while for the most peripheral (80-90%)
we find $230\pm 38$. This corresponds to an increase of $(27\pm4)\%$ over the
results at $\sqrt{s_{\mathrm{NN}}}=2.76\,\mathrm{Te\kern-.25exV}$ previously
reported by ALICE. The energy dependence of the total number of charged
particles produced in heavy-ion collisions is found to obey a modified
power-law like behaviour. The charged-particle pseudorapidity density of the
most central collisions is compared to model calculations --- none of which
fully describes the measured distribution. We also present an estimate of the
rapidity density of charged particles. The width of that distribution is found
to exhibit a remarkable proportionality to the beam rapidity, independent of
the collision energy from the top SPS to LHC energies.
