Coherent production of J/psi mesons is studied in lead-lead collision data at a nucleon-nucleon centre-of-mass energy of 5 TeV collected by the LHCb experiment. The data set corresponds to an integrated luminosity of about 10 mu b(-1). The J/psi, mesons are reconstructed in the dimuon final state, where the muons are detected within the pseudorapidity region 2.0 < eta < 4.5. The J/psi mesons are required to have transverse momentum P-T < 1 GeV and rapidity 2.0 < y < 4.5. The cross-section within this fiducial region is measured to be sigma = 5.3 +/- 0.2 (stat) +/- 0.5 (syst) +/- 0.7 (lumi) mb. The differential cross-section is also measured in five bins of J/psi rapidity. The results are compared to predictions from phenomenological models.