We present a magnetic manipulation system capable of 5 degree-of-freedom (5-DOF) wireless control of micro- and nanostructures (3-DOF position, 2-DOF pointing orientation). The system has a spherical workspace with a diameter of approximately 10 mm, and is completely unrestrained in the rotational degrees-of-freedom. This is accomplished through the superposition of multiple magnetic fields, and capitalizes on a linear representation of the coupled field contributions of multiple soft-magnetic-core electromagnets acting in concert. The system consists of 8 stationary electromagnets with ferromagnetic cores, and is capable of producing arbitrary magnetic fields and field gradients up to 50 mT and 5 T/m at frequencies up to 2 kHz. The capabilities of the system are evaluated through the introduction of the reachable magnetic workspace of the system as well as frequency response and calibration results. Experimental results are presented which demonstrate different magnetic control strategies at sub-mm and sub-μm scale.