Stars that escape globular clusters form tidal tails that are predominantly shaped by the global distribution of mass in the Galaxy, but also preserve a historical record of small-scale perturbations. Using deep grz photometry from DECaLS, we present highly probable members of the tidal tails associated with the evaporating globular cluster Palomar 5. These data yield the cleanest view of a stellar stream beyond ≈20 kpc and reveal: (1) a wide, low surface-brightness extension of the leading tail; (2) significant density variations along the stream; and (3) sharp changes in the direction of both the leading and the trailing tail. In the fiducial Milky Way model, a rotating bar perturbs the Palomar 5 tails and can produce streams with similar width and density profiles to those observed. However, the deviations of the stream track in this simple model do not match those observed in the Palomar 5 trailing tail, indicating the need for an additional source of perturbation. These discoveries open up the possibility of measuring the population of perturbers in the Milky Way, including dark-matter subhalos, with an ensemble of stellar streams and deep photometry alone.