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 $w_p(r_p)$ measured by using 3022 galaxies with robust spectroscopic redshifts in two independent fields (COSMOS and VVDS-02h) covering in total 0.8 deg$^2$. We quantify how the scale dependent clustering amplitude $r_0$ changes with redshift making use of mock samples to evaluate and correct the survey selection function. Using a power-law model $xi(r) = (r/r_0)^{-gamma}$ we find that the correlation function for the general population is best fit by a model with a clustering length $r_0$=3.95$^{+0.48}_{-0.54}$ h$^{-1}$Mpc and slope $gamma$=1.8$^{+0.02}_{-0.06}$ at $z$~2.5, $r_0$=4.35$pm$0.60 h$^{-1}$Mpc and $gamma$=1.6$^{+0.12}_{-0.13}$ at $z$~3.5. We use these clustering parameters to derive the large-scale linear galaxy bias $b_L^{PL}$, between galaxies and dark matter. We find $b_L^{PL}$ = 2.68$pm$0.22 at redshift $z$~3 (assuming $sigma_8$ = 0.8), significantly higher than found at intermediate and low redshifts. We fit an HOD model to the data and we obtain that the average halo mass at redshift $z$~3 is $M_h$=10$^{11.75pm0.23}$ h$^{-1}$M$_{odot}$. From this fit we confirm that the large-scale linear galaxy bias is relatively high at $b_L^{HOD}$ = 2.82$pm$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 ($M_r$<-21.5) galaxy population which typically occupy haloes of mass $langle M_hrangle$ = 10$^{13.9}$ h$^{-1}$ $M_{odot}$ at redshift $z$=0.
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