A search for narrow, high-mass resonances decaying to electron or muon pairs has been performed using pp collision data collected at s=7TeV by the CMS experiment in 2011. The data sample corresponds to an integrated luminosity of approximately 5 fb−1. The event yields observed in the signal regions are consistent with predictions of the standard model backgrounds, and upper limits on the cross section times branching fraction for a resonance decaying to dileptons are extracted from a shape analysis of the dilepton invariant mass distribution. The resulting mass limits at 95% confidence level are 2330 GeV for the Z′ in the Sequential Standard Model, 2000 GeV for the superstring-inspired Zψ′ resonance, 890 (540) GeV for the Stueckelberg extension ZSt′ with the mass parameter ϵ=0.06 (0.04), and 2140 (1810) GeV for Kaluza–Klein gravitons with the coupling parameter k/M¯Pl of 0.10 (0.05). These limits are the most stringent to date.