Results are presented from a search for new physics in the final state containing a photon (gamma) and missing transverse energy (is not an element of(T)). The data correspond to an integrated luminosity of 5.0 fb(-1) collected in pp collisions at root s = 7 TeV by the CMS experiment. The observed event yield agrees with standard-model expectations for the gamma + is not an element of(T) events. Using models for the production of dark-matter particles (chi), we set 90% confidence level (C. L.) upper limits of 13.6-15.4 fb on chi production in the gamma + is not an element of(T) state. These provide the most sensitive upper limits for spin-dependent chi-nucleon scattering for chi masses (M-chi) between 1 and 100 GeV. For spin-independent contributions, the present limits are extended to M-chi < 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.