Results are presented from a search for new physics in the final state containing a photon (γ) and missing transverse energy (E̸T). The data correspond to an integrated luminosity of 5.0 fb-1 collected in pp collisions at √s=7 TeV by the CMS experiment. The observed event yield agrees with standard-model expectations for the γ+E̸T events. Using models for the production of dark-matter particles (χ), we set 90% confidence level (C.L.) upper limits of 13.6–15.4 fb on χ production in the γ+E̸T state. These provide the most sensitive upper limits for spin-dependent χ-nucleon scattering for χ masses (Mχ) between 1 and 100 GeV. For spin-independent contributions, the present limits are extended to Mχ<3.5 GeV. For models with 3–6 large extra dimensions, our data exclude extra-dimensional Planck scales between 1.64 and 1.73 TeV at 95% C.L.