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We present the charged-particle pseudorapidity density in Pb-Pb collisions at sNN−−−√=5.02TeV 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 21400±1300 while for the most peripheral (80-90%) we find 230±38. This corresponds to an increase of (27±4)% over the results at sNN−−−√=2.76TeV 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.