During the first 500 million years of cosmic history, the first stars and galaxies formed, seeding the Universe with heavy elements and eventually reionizing the intergalactic medium1-3. Observations with the James Webb Space Telescope (JWST) have uncovered a surprisingly high abundance of candidates for early star-forming galaxies, with distances (redshifts, z), estimated from multiband photometry, as large as z ≈ 16, far beyond pre-JWST limits4-9. Although such photometric redshifts are generally robust, they can suffer from degeneracies and occasionally catastrophic errors. Spectroscopic measurements are required to validate these sources and to reliably quantify physical properties that can constrain galaxy formation models and cosmology10. Here we present JWST spectroscopy that confirms redshifts for two very luminous galaxies with z > 11, and also demonstrates that another candidate with suggested z ≈ 16 instead has z = 4.9, with an unusual combination of nebular line emission and dust reddening that mimics the colours expected for much more distant objects. These results reinforce evidence for the early, rapid formation of remarkably luminous galaxies while also highlighting the necessity of spectroscopic verification. The large abundance of bright, early galaxies may indicate shortcomings in current galaxy formation models or deviations from physical properties (such as the stellar initial mass function) that are generally believed to hold at later times.