At a distance of 23.2 kpc from the Sun and of 16.6 kpc above the Galactic plane, Palomar 5 is a halo globular cluster characterized by very low total mass, a large core radius and low central concentration. This cluster shows two massive tidal tails characterized by stellar density gaps (underdense regions) and clumps (overdense regions). By means of direct N-body simulations and simplified numerical models, we studied the formation and characteristics of the tidal tails around Palomar 5, along its orbit in the Milky Way potential. Unlike previous findings, we are able to reproduce the substructures observed in the stellar streams of this cluster, without including any lumpiness in the dark matter halo. Here we show that overdensities similar to those observed in Palomar 5 can be reproduced by the epicyclic motion of stars along Palomar 5 tails, i.e. a simple local accumulation of orbits of stars escaped from the cluster with very similar initial positions and velocities. This process is able to form stellar clumps at distances of several kiloparsecs from the cluster, so it is not a phenomenon confined to the inner part of Palomar 5’s tails, as previously suggested. Our models can reproduce the density contrast between the clumps and the surrounding tails found in the observed streams, without including any lumpiness in the dark halo, suggesting new upper limits on its granularity.