Aims. We investigate the production efficiency of ionizing photons (ξion∗) of 1174 galaxies with secure redshift at z=2 - 5 from the VANDELS survey to determine the relation between ionizing emission and physical properties of bright and massive sources. Methods. We constrained ξion∗ and galaxy physical parameters by means of spectrophotometric fits performed with the BEAGLE code. The analysis exploits the multi-band photometry in the VANDELS fields and the measurement of UV rest-frame emission lines (CIII]λ1909, HeIIλ1640, and OIII]λ1666) from deep VIMOS spectra. Results. We find no clear evolution of ξion∗ with redshift within the probed range. The ionizing efficiency slightly increases at fainter MUV and bluer UV slopes, but these trends are less evident when the analysis is restricted to a complete subsample at log(Mstar/M⊙) > 9.5. We find a significant trend of increasing ξion∗ with increasing EW(Lyα), with an average log(ξion∗/Hz erg-1) > 25 at EW > 50 Åand a higher ionizing efficiency for high-EW CIII]λ1909 and OIII]λ1666 emitters. The most significant correlations are found with respect to stellar mass, specific star formation rate (sSFR), and SFR surface density (ΣSFR). The relation between ξion∗ and sSFR increases monotonically from log(ξion∗/Hz erg-1)~24.5 at log(sSFR)~-9.5yr-1 to ~25.5 at log(sSFR)~-7.5yr-1. This relation has a low scatter and only a weak dependence on mass. The objects above the main sequence of star formation consistently have higher than average ξion∗. A clear increase in ξion∗ with ΣSFR is also found, with log(ξion∗/Hz erg-1) > 25 for objects at ΣSFR>10M⊙ yr-1 kpc-2. Conclusions. Bright (MUV≲20) and massive (log(Mstar/M⊙)≳9.5) galaxies at z=2 - 5 have a moderate ionizing efficiency. However, the correlation between ξion∗ and sSFR, together with the known increase in the average sSFR with redshift at fixed stellar mass, suggests that similar galaxies in the epoch of reionization can be efficient sources of ionizing photons. The availability of sSFR and ΣSFR as proxies for ξion∗ can be fundamentally important in determining the role of galaxy populations at z≳10 that were recently discovered by the James Webb Space Telescope in the onset of reionization.