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The pseudorapidity density of charged particles (dNch/dη) at mid-rapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of sNN−−−√ = 5.02 TeV. It increases with centrality and reaches a value of 1943±54 in |η|<0.5 for the 5% most central collisions. A rise in dNch/dη as a function of sNN−−−√ for the most central collisions is observed, steeper than that observed in proton-proton collisions and following the trend established by measurements at lower energy. The centrality dependence of dNch/dη as a function of the average number of participant nucleons, ⟨Npart⟩, calculated in a Glauber model, is compared with the previous measurement at lower energy. A constant factor of about 1.2 describes the increase in 2⟨Npart⟩⟨dNch/dη⟩ from sNN−−−√ = 2.76 TeV to sNN−−−√ = 5.02 TeV for all centrality intervals, within the measured range of 0-80% centrality. The results are also compared to models based on different mechanisms for particle production in nuclear collisions.