This article presents narrow-band Hα and [OIII] images of the interacting pair of galaxies NGC 5953 (with a Seyfert type 2 nucleus) and NGC 5954 (with a LINER). Long-slit spectroscopy, from [NeV] lambda3425A to [SIII] lambda9532A, at intermediate resolution along position angles 44 deg and 182 deg through the nucleus of NGC 5953, is also presented. Both objects show a recent burst of star formation in the circumnuclear region, more conspicuous in NGC 5953. The HII regions are photoionized by a cluster of stars with effective temperature 42000K the ionized gas has a metallicity of three times the solar value, with an overabundance of nitrogen. In the north-eastern part of the nucleus of NGC 5953 there is extended circumnuclear emission produced by a mixture of low- and high-excitation gas, which is kinematically perturbed; this probably reflects photoionization by stars and by an additional source, which may be identified with radiation escaping from the nucleus and/or ionization related to the radio jet, which has a geometry closely related to the line emission. A problem is identified with the line ratios involving the infrared [SIII] lines, which may reflect a problem with the sulphur atomic parameters, depletion of the sulphur abundance or the inadequacy of one-component photoionization models to reproduce the observed line ratios.