The central 13'' of NGC 5728 have been observed using a bidimensional array of optical fibers providing simultaneous spatial and spectral information. The present data have been used to analyze the morphology and kinematics of the circumnuclear environment of this galaxy. The region emitting double-peaked lines, previously reported by others, extends around 3.5'' in the northeast direction starting from the kinematical nucleus. The blue component of these lines, with widths of order of those found in the circumnuclear zone, resembles the general behavior of the galaxy, being regularly fitted by the galactic mean velocity field. The red component has larger line widths and fluxes and is probably related to the nucleus. We suggest that this component represents outflow produced by nuclear activity. The kinematical center coincides with the peak in radio emission, but is separated by about 1'' from the maxima of the Halpha, [N II], and [S II] emission, which strongly suggests that the active nucleus is obscurred. This result explains the nuclear redshift and the high ratio of circumnuclear to nuclear flux emission reported by other authors. The electron density derived from the sulfur line ranges from 10(2.0) to 10(2.8) cm-3 in the innermost zones, and its distribution is aligned in the same direction (P.A. approximately 123-degrees) as the line intensity and radio maps. The observed line intensity ratios in the innermost part are not compatible with solar metallicity models in the range of densities derived from the sulfur lines. Overabundances of N and S, together with the presence of dust, could explain this discrepancy. With the sole exception of the red component of the double-peaked spectra, the dependence of line widths on galactocentric distance is a smoothly decaying function, supporting the existence of a single kinematical mechanism (likely to be the local velocity dispersion of the gas clouds) causing the broadening of the lines.