Thin stellar streams, formed from the tidal disruption of globular clusters, are important gravitational tools, sensitive to both global and small-scale properties of dark matter. The Palomar 5 stellar stream (Pal 5) is an exemplar stream within the Milky Way: its ~20{deg} tidal tails connect back to the progenitor cluster, and the stream has been used to study the shape, total mass, and substructure fraction of the dark matter distribution of the Galaxy. However, most details of the phase-space distribution of the stream are not fully explained, and dynamical models that use the stream for other inferences are therefore incomplete. Here we aim to measure distance and kinematic properties along the Pal 5 stream in order to motivate improved models of the system. We use a large catalog of RR Lyrae-type stars (RRLs) with astrometric data from the Gaia mission to probabilistically identify RRLs in the Pal 5 stream. RRLs are useful because they are intrinsically luminous standard candles and their distances can be inferred with small relative precision (~3%). By building a probabilistic model of the Pal 5 cluster and stream in proper motion and distance, we find 27 RRLs consistent with being members of the cluster (10) and stream (17). Using these RRLs, we detect gradients in distance and proper motion along the stream, and provide an updated measurement of the distance to the Pal 5 cluster using the RRLs, d=20.6+/-0.2 kpc. We provide a catalog of Pal 5 RRLs with inferred membership probabilities for future modeling work.