We investigate the evolution of galaxy clustering for galaxies in the redshift range 2.0 <z< 5.0 using the VIMOS Ultra Deep Survey (VUDS). We present the projected (real-space) two-point correlation function wp(rp) measured by using 3022 galaxies with robust spectroscopic redshifts in two independent fields (COSMOS and VVDS-02h) covering in total 0.8deg2. We quantify how the scale dependent clustering amplitude r0 changes with redshift making use of mock samples to evaluate and correct the survey selection function. Using a power-law model ξ(r) = (r/r0)− γ we find that the correlation function for the general population is best fit by a model with a clustering length r0 = 3.95+0.48-0.54 h-1 Mpc and slope γ = 1.8+0.02-0.06 at z ~ 2.5, r0 = 4.35 ± 0.60 h-1 Mpc and γ = 1.6+0.12-0.13 at z ~ 3.5. We use these clustering parameters to derive the large-scale linear galaxy bias bLPL, between galaxies and dark matter. We find bLPL = 2.68 ± 0.22 at redshift z ~ 3 (assuming σ8 = 0.8), significantly higher than found at intermediate and low redshifts for the similarly general galaxy populations. We fit a halo occupation distribution (HOD) model to the data and we obtain that the average halo mass at redshift z ~ 3 is Mh = 1011.75 ± 0.23 h-1M⊙. From this fit we confirm that the large-scale linear galaxy bias is relatively high at bLHOD = 2.82 ± 0.27. Comparing these measurements with similar measurements at lower redshifts we infer that the star-forming population of galaxies at z ~ 3 should evolve into the massive and bright (Mr< −21.5)galaxy population, which typically occupy haloes of mass ⟨ Mh ⟩ = 1013.9 h-1M⊙ at redshift z = 0.