We study the morphologies and sizes of galaxies at z ≥ 5 using high-resolution cosmological zoom-in simulations from the Feedback In Realistic Environments project. The galaxies show a variety of morphologies, from compact to clumpy to irregular. The simulated galaxies have more extended morphologies and larger sizes when measured using rest-frame optical B-band light than rest-frame UV light; sizes measured from stellar mass surface density are even larger. The UV morphologies are usually dominated by several small, bright young stellar clumps that are not always associated with significant stellar mass. The B-band light traces stellar mass better than the UV, but it can also be biased by the bright clumps. At all redshifts, galaxy size correlates with stellar mass/luminosity with large scatter. The half-light radii range from 0.01 to 0.2 arcsec (0.05–1 kpc physical) at fixed magnitude. At z ≥ 5, the size of galaxies at fixed stellar mass/luminosity evolves as (1 + z)−m, with m ∼ 1–2. For galaxies less massive than M* ∼ 108 M⊙, the ratio of the half-mass radius to the halo virial radius is ∼10 per cent and does not evolve significantly at z = 5–10; this ratio is typically 1–5 per cent for more massive galaxies. A galaxy's ‘observed’ size decreases dramatically at shallower surface brightness limits. This effect may account for the extremely small sizes of z ≥ 5 galaxies measured in the Hubble Frontier Fields. We provide predictions for the cumulative light distribution as a function of surface brightness for typical galaxies at z = 6.