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 similar to 145 arcmin(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 similar to 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-circle dot) 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. All data products, including the literature compilation, are made publicly available.