The electronic structure and the magnetism of the novel ferromagnetic semiconductor (Ga,Fe)Sb, whose Curie temperature $T_{rm C}$ can exceed room temperature, were investigated by means of x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD), and resonance photoemission spectroscopy (RPES). The line-shape analyses of the XAS and XMCD spectra suggest that the ferromagnetism is of intrinsic origin. The orbital magnetic moments deduced using XMCD sum rules were found to be large, indicating that there is a considerable amount of 3$d^{6}$ contribution to the ground state of Fe. From RPES, we observed a strong dispersive Auger peak and non-dispersive resonantly enhanced peaks in the valence-band spectra. The latter is a fingerprint of the correlated nature of Fe 3$d$ electrons, whereas the former indicates their itinerant nature. It was also found that the Fe 3$d$ states have finite contribution to the DOS at the Fermi energy. These states presumably consisting of majority-spin $p$-$d$ hybridized states or minority-spin $e$ states would be responsible for the ferromagnetic order in this material.