The present invention discloses microporous UZM-5 zeolite membranes, methods for making the same, and methods of separating gases, vapors, and liquids using the same. The small-pore microporous UZM-5 zeolite membrane is prepared by two different methods, including in-situ crystallization of one or more layers of UZM-5 zeolite crystals on a porous membrane support, and a seeding method by in-situ crystallization of a continuous second layer of UZM-5 zeolite crystals on a seed layer of UZM-5 zeolite crystals supported on a porous membrane support. The membranes in the form of disks, tubes, or hollow fibers have superior thermal and chemical stability, good erosion resistance, high CO2 plasticization resistance, and significantly improved selectivity over polymer membranes for gas, vapor, and liquid separations.