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The James Webb Space Telescope provides an unprecedented opportunity for unbiased surveys of H α -emitting galaxies at z > 4 with the NIRCam's wide-field slitless spectroscopy (WFSS). In this work, we present a census of Ly α escape fraction ( f _esc,Ly _α ) of 165 star-forming galaxies at z = 4.9–6.3, utilizing their H α emission directly measured from FRESCO NIRCam/WFSS data. We search for Ly α emission of each H α -emitting galaxy in the Very Large Telescope/MUSE data. The overall f _esc,Ly _α measured by stacking is 0.090 ± 0.006. We find that f _esc,Ly _α displays a strong dependence on the observed UV slope ( β _obs ) and E ( B − V ), such that the bluest galaxies ( β _obs ∼ −2.5) have the largest escape fractions ( f _esc,Ly _α ≈ 0.6), indicative of the crucial role of dust and gas in modulating the escape of Ly α photons. f _esc,Ly _α is less well related to other parameters, including the UV luminosity and stellar mass, and the variation in f _esc,Ly _α with them can be explained by their underlying coupling with E ( B − V ) or β _obs . Our results suggest a tentative decline in f _esc,Ly _α at z ≳ 5, implying increasing intergalactic medium attenuation toward higher redshift. Furthermore, the dependence of f _esc,Ly _α on β _obs is proportional to that of the ionizing photon escape fraction ( f _esc,LyC ), indicating that the escape of Ly α and ionizing photon may be regulated by similar physical processes. With f _esc,Ly _α as a proxy to f _esc,LyC , we infer that UV-faint ( M _UV > −16) galaxies contribute >70% of the total ionizing emissivity at z = 5–6. If these relations hold during the epoch of reionization, UV-faint galaxies can contribute the majority of UV photon budget to reionize the Universe.