ABSTRACT We describe JWST/NIRSpec prism measurements of Ly α emission in z ≳ 5 galaxies. We identify Ly α detections in 10 out of 69 galaxies with robust rest-optical emission-line redshift measurements at 5 ≤ z < 7 in the Cosmic Evolution Early Release Science (CEERS) and DDT-2750 observations of the Extended Groth Strip field. Galaxies at z ≃ 6 with faint continuum (F150W=27–29 mag) are found with extremely large rest-frame Ly α equivalent widths (EWs; ranging up to 286 Å). Likely Ly α detections are also seen in two new z > 7 galaxies (z = 7.49 and 7.17) from the second epoch of CEERS observations, both showing large Ly α EWs that likely indicate significant transmission through the intergalactic medium (IGM). We measure high Ly α escape fractions in the 12 Ly α emitters in our sample (median 0.28), two of which show $f_{\rm esc}^{ {\rm Ly}\alpha }$ near unity (>0.80). We find that $50_{-11}^{+11}$ per cent of z ≃ 6 galaxies with [O iii] + H β EW>1000 Å have $f_{\rm esc}^{ {\rm Ly}\alpha }$ >0.2, consistent with the fractions found in lower redshift samples with matched [O iii] + H β EWs. While uncertainties are still significant, we find that only $10_{-5}^{+9}$ per cent of z > 7 galaxies with similarly strong rest optical emission lines show such large $f_{\rm esc}^{ {\rm Ly}\alpha }$, as may be expected if IGM attenuation of Ly α increases towards higher redshifts. We identify photometric galaxy overdensities near the z ≳ 7 Ly α emitters, potentially providing the ionizing flux necessary to create large ionized sightlines that facilitate Ly α transmission. Finally, we investigate the absence of Ly α emission in a comparable (and spectroscopically confirmed) galaxy overdensity at z = 7.88 in the Abell 2744 field, discussing new prism spectra of the field obtained with the UNCOVER program.