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The Advanced Photon Source (APS) at Argonne National Laboratory is considering the development of a superconducting linac-based fourth-generation hard X-ray source to meet future scientific needs of the hard X-ray user community. This work specifically focuses on the design of an optimized 5-cell superconducting radio-frequency structure well suited for a high-energy, high-beam-current energy recovery linac. The cavity design parameters are based on the APS storage ring nominal 7 GeV and 100 mA beam operation. A high-current 5-cell cw superconducting cavity operating at 1.4 GHz has been designed. In order to achieve a high current, the accelerating cavity shape has been optimized and large end-cell beam pipes have been adopted. The beam break-up threshold of the cavity has been estimated using the code TDBBU, which predicts a high threshold beam current for a 7 GeV energy recovery linac model. A copper prototype cavity has been fabricated that uses half-cell modules, initially assembled by clamping the cells together.