We present the results of the VLT/VIMOS integral-field spectroscopic observations of the inner 28 × 28 arcsec2 (3.1 × 3.1 kpc2) of the interacting spiral NGC 5719, which is known to host two cospatial counter-rotating stellar discs. At each position in the field of view, the observed galaxy spectrum is decomposed into the contributions of the spectra of two stellar and one ionized-gas components. We measure the kinematics and the line strengths of the Lick indices of the two stellar counter-rotating components. We model the data of each stellar component with single stellar population models that account for the α/Fe overabundance. We also derive the distribution and kinematics of the ionized-gas disc, that is associated with the younger, less rich in metals, more α-enhanced, and less luminous stellar component. They are both counter rotating with respect the main stellar body of the galaxy. These findings prove the scenario where gas was accreted first by NGC 5719 on to a retrograde orbit from the large reservoir available in its neighbourhoods as a result of the interaction with its companion NGC 5713, and subsequently fuelled the in situ formation of the counter-rotating stellar disc.