  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 $\sim 20^\circ$ 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
($\sim3\%$). 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, $d = 20.6 \pm
0.2~\textrm{kpc}$. We provide a catalog of Pal 5 RRLs with inferred membership
probabilities for future modeling work.
