The pseudorapidity density of charged particles, dNch=dη, at midrapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of √sNN=5.02 TeV. For the 5% most central collisions, we measure a value of 1943±54. The rise in dNch=dη as a function of √sNN is steeper than that observed in proton-proton collisions and follows the trend established by measurements at lower energy. The increase of dNch=dη as a function of the average number of participant nucleons, hNparti, calculated in a Glauber model, is compared with the previous measurement at √sNN=2.76 TeV. A constant factor of about 1.2 describes the increase in dNch=dη from √sNN=2,76 to 5.02 TeV for all centrality classes, 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.