We present the results of the VLT/VIMOS integral-field spectroscopic observations of the inner 28x28 (3.1 kpc x 3.1 kpc) of the interacting spiral NGC 5719, which is known to host two co-spatial 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 ionised-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 alpha/Fe overabundance. We also derive the distribution and kinematics of the ionised-gas disc, that is associated with the younger, less rich in metals, more alpha-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 onto a retrograde orbit from the large reservoir available in its neighbourhoods as the result of the interaction with its companion NGC 5713, and subsequently fuelled the in situ formation of the counter-rotating stellar disc.