The NGC 5903 galaxy group is a nearby (~30 Mpc) system of ~30 members, dominated by the giant ellipticals NGC 5903 and NGC 5898. The group contains two unusual structures, a ~110 kpc long HI filament crossing NGC 5903, and a ~75 kpc wide diffuse, steep-spectrum radio source of unknown origin which overlaps NGC 5903 and appears to be partly enclosed by the HI filament. Using a combination of Chandra, XMM-Newton, GMRT and VLA observations, we detect a previously unknown ~0.65 keV intra-group medium filling the volume within 145 kpc of NGC 5903, and find a loop of enhanced X-ray emission extending ~35 kpc southwest from the galaxy, enclosing the brightest part of the radio source. The northern and eastern parts of this X-ray structure are also strongly correlated with the southern parts of the HI filament. We determine the spectral index of the bright radio emission to be $alpha_{150}^{612}$=1.03$pm$0.08, indicating a radiative age >360 Myr. We discuss the origin of the correlated radio, X-ray and HI structures, either through an interaction-triggered AGN outburst with enthalpy 1.8x10$^{57}$ erg, or via a high-velocity collision between a galaxy and the HI filament. While neither scenario provides a complete explanation, we find that an AGN outburst is the most likely source of the principal X-ray and radio structures. However, it is clear that galaxy interactions continue to play an important role in the development of this relatively highly evolved galaxy group. We also resolve the question of whether the group member galaxy ESO 514-3 hosts a double-lobed radio source, confirming that the source is a superposed background AGN.