Hydrodynamic fluidity in condensed matter physics has been experimentally demonstrated only in a limited number of compounds due to the stringent conditions that must be met. Herein, we demonstrate phonon hydrodynamic-like properties in three-dimensional topological semimetal ZrTe5 thanks to its ultrahigh-purity and intrinsic structural instability. By measuring the thermal properties in a wide temperature range, two representative experimental evidences of phonon hydrodynamics are seen in an interesting temperature window between the ballistic and diffusive regimes: a faster evolution of the thermal conductivity than in the ballistic regime and the non-monotonic temperature-dependent effective phonon mean-free-path. In addition, magneto-thermal conductivity results indicate us that charged quasiparticles, as well as phonons, may also play an important role in the hydrodynamic flow in the ZrTe5 system.