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ABSTRACT JWST has recently sparked a new era of Lyα spectroscopy, delivering the first measurements of the Lyα escape fraction and velocity profile in typical galaxies at z ≃ 6−10. These observations offer new prospects for insight into the earliest stages of reionization. But to realize this potential, we need robust models of Lyα properties in galaxies at z ≃ 5−6 when the IGM is mostly ionized. Here, we use new JWST observations from the JADES and FRESCO surveys combined with VLT/MUSE and Keck/DEIMOS data to characterize statistical distributions of Lyα velocity offsets, escape fractions, and EWs in z ≃ 5−6 galaxies. We find that galaxies with large Lyα escape fractions (>0.2) are common at z ≃ 5−6, comprising 30 per cent of Lyman break selected samples. Comparing to literature studies, our census suggests that Lyα becomes more prevalent in the galaxy population towards higher redshift from z ∼ 3 to z ∼ 6, although we find that this evolution slows considerably between z ∼ 5 and z ∼ 6, consistent with modest attenuation from residual H i in the mostly ionized IGM at z ≃ 5−6. We find significant evolution in Lyα velocity profiles between z ≃ 2−3 and z ≃ 5−6, likely reflecting the influence of resonant scattering from residual intergalactic H i on the escape of Lyα emission near line centre. This effect will make it challenging to use Lyα peak offsets as a probe of Lyman continuum leakage at z ≃ 5−6. We use our z ≃ 5−6 Lyα distributions to make predictions for typical Lyα properties at z ≳ 8 and discuss implications of a recently discovered Lyα emitter at z ≃ 8.5 with a small peak velocity offset (156 km s−1).