Direct detection of dark matter in SU(5) x U(1) supergravity

We compute the scattering rates for the lightest neutralino \chi^0_1 in the forthcoming germanium (^{73}{\rm Ge}+^{76}{\rm Ge}) detector and a proposed lead detector (^{207}{\rm Pb}), within the framework of SU(5)\times U(1) supergravity. We find that in only a small portion (\lsim10\%) of the parameter spaces of this class of models, are the rates in the germanium detector above the expected initial experimental sensitivity of 0.1 events/kg/day. However, a much larger portion (\lsim40\%) of the parameter spaces could be probed with an improved background rejection capability (0.01 events/kg/day) and/or a more sensitive detector (^{207}{\rm Pb}).