We present the results of a systematic search for candidate quiescent galaxies in the distant universe in 11 JWST fields with publicly available observations collected during the first 3 months of operations and covering an effective sky area of ~145arcmin^2^. We homogeneously reduce the new JWST data and combine them with existing observations from the Hubble Space Telescope. We select a robust sample of ~80 candidate quiescent and quenching galaxies at 3<z<5 using two methods: (1) based on their rest-frame UVJ colors, and (2) a novel quantitative approach based on Gaussian mixture modeling of the near-UV-U, U-V, and V-J rest-frame color space, which is more sensitive to recently quenched objects. We measure comoving number densities of massive (M_*_>=10^10.6^M_{sun}_) quiescent galaxies consistent with previous estimates relying on ground-based observations, after homogenizing the results in the literature with our mass and redshift intervals. However, we find significant field-to-field variations of the number densities up to a factor of 2-3, highlighting the effect of cosmic variance and suggesting the presence of overdensities of red quiescent galaxies at z>3, as could be expected for highly clustered massive systems. Importantly, JWST enables the robust identification of quenching/quiescent galaxy candidates at lower masses and higher redshifts than before, challenging standard formation scenarios.