We report a spatial resolution of 5.4 nm in images of sarcoplasmic reticulum from rabbit muscle. The images were obtained in an aberration-corrected photoemission electron microscope with a hyperbolic mirror as the correcting element for spherical and chromatic aberration. In-situ measurements and numerical simulations confirm the low residual aberration in the instrument and indicate the ultimate resolution in this type of microscopy to be below 2 nm.