We present a VLT/MUSE survey of lensed high-redshift galaxies behind the z=0.77 cluster RCS0224-0002. We study the detailed internal properties of a highly magnified ({mu}~29) z=4.88 galaxy seen through the cluster. We detect wide-spread nebular CIV{lambda}{lambda}1548,1551{AA} emission from this galaxy as well as a bright Ly{alpha} halo with a spatially-uniform wind and absorption profile across 12 kpc in the image plane. Blueshifted high- and low-ionisation interstellar absorption indicate the presence of a high-velocity outflow ({Delta}v~300 km/s) from the galaxy. Unlike similar observations of galaxies at z=2-3, the Ly{alpha} emission from the halo emerges close to the systemic velocity - an order of magnitude lower in velocity offset than predicted in shell-like outflow models. To explain these observations we favour a model of an outflow with a strong velocity gradient, which changes the effective column density seen by the Ly{alpha} photons. We also search for high-redshift Ly{alpha} emitters and identify 14 candidates between z=4.8-6.6, including an over-density at z=4.88, of which only one has a detected counterpart in HST/ACS+WFC3 imaging.