Palomar 5 is one of the sparsest star clusters in the Galactic halo and is best known for its spectacular tidal tails, spanning over 20 degrees across the sky. With N-body simulations, we show that both distinguishing features can result from a stellar-mass black hole population, comprising similar to 20% of the present-day cluster mass. In this scenario, Palomar 5 formed with a 'normal' black hole mass fraction of a few per cent, but stars were lost at a higher rate than black holes, such that the black hole fraction gradually increased. This inflated the cluster, enhancing tidal stripping and tail formation. A billion years from now, the cluster will dissolve as a 100% black hole cluster. Initially denser clusters end up with lower black hole fractions, smaller sizes and no observable tails. Black hole-dominated, extended star clusters are therefore the likely progenitors of the recently discovered thin stellar streams in the Galactic halo.