This paper describes design, construction, and testing of a 5 kJ Superconducting Magnetic Energy Storage (SMES) magnet. This magnet was built by American Superconductor Corporation(ASC) for Gesellschaft fur Innovative Energieumwandlung und Speicherung (EUS) of Germany. The magnet consists of a solenoidal coil constructed from a silver-sheathed BiPb2Sr2Ca2Cu3O (Bi-2223) conductor which was reacted before winding. The coil is epoxy impregnated and cooled with single stage Gifford McMahon (G-M) cryocoolers for operation at 100 A (DC) with substantial AC components due to the frequent variation of current (ramp-up and ramp-down.) The dominant heat load in the magnet is eddy-current heating caused by the current ramping operation, To accommodate this heat load, a separate cryocooler is employed for cooling the main coil. A smaller capacity cryocooler is used for intercepting the heat load of the conduction cooled current leads. Specialized thermal interfaces were developed for operation in AC field and at high voltages. The magnet can be ramped from zero to 100 A in 2 s and back to zero current in 2 s. One hundred sequential ramp-up/ramp-down cycles can be accommodated before the magnet temperature exceeds the allowable maximum. The magnet was tested in early spring of 1996 and was shipped to EUS in mid June, The successful operation of this magnet illustrates that the technology of cooling HTS magnets with G-M type cryocooler is now fully established. The long term operation of this magnet at EUS will verify the reliability of HTS magnet system in critical applications and will open future applications for HTS in the area of SMES and other magnets.