We extensively characterize the electronic structure of ultra-narrow graphene nanoribbons (GNRs) with armchair edges and zig-zag termini that have 5 carbon atoms across their width (5-AGNRs), as synthesised on Au(111). Scanning tunnelling spectroscopy measurements on the ribbons, recorded on both the metallic substrate and a decoupling NaCl layer, show well-defined dispersive bands and in-gap states. In combination with theoretical calculations, we show how these in-gap states are topological in nature and localised at the zig-zag termini of the nanoribbons. Besides rationalising the driving force behind the topological class selection of 5-AGNRs, we also uncover the length-dependent behaviour of these end states which transition from singly occupied spin-split states to a closed-shell form as the ribbons become shorter. Finally, we demonstrate the magnetic character of the end states via transport experiments in a model two-terminal device structure in which the ribbons are suspended between the scanning probe and the substrate that both act as leads.