Results are presented from a search for new physics in which the final state contains a photon (γ) and missing transverse energy (ME_T). The data correspond to an integrated luminosity of 5.0 fb⁻¹ (inverse femtobarns) collected in pp collisions at √s = 7 TeV by the CMS experiment. The observed event yield agrees with Standard-Model expectations for γ+ME_T events. Using models for production of dark-matter particles (represented by the Greek letter χ), we set 90% confidence level (CL) upper limits of 13.6–15.4 fb on χ production in the γ+ME_T state. These provide the most sensitive upper limits for spin-dependent χ-nucleon scattering for χ masses between 1 and 100 GeV. For spin-independent contributions, the present limits are extended to χ masses below 3.5 GeV. For models with 3–6 large extra dimensions, our data exclude extra-dimensional Planck scales between 1.65 and 1.71 TeV at 95% CL.