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Time- and angle-resolved photoemission spectroscopy (TrARPES) is a powerful technique for capturing the ultrafast dynamics of charge carriers and revealing photo-induced phase transitions in quantum materials. However, the lack of widely tunable probe photon energy, which is critical for accessing the dispersions at different out-of-plane momentum $k_z$ in TrARPES measurements, has hindered the ultrafast dynamics investigation of 3D quantum materials such as Dirac or Weyl semimetals. Here we report the development of a TrARPES system with a highly tunable probe photon energy from 5.3 to 7.0 eV. The tunable probe photon energy is generated by the fourth harmonic generation of a tunable wavelength femtosecond laser source by combining a $\beta$-BaB$_2$O$_4$ (BBO) crystal and a KBe$_2$BO$_3$F$_2$ (KBBF) crystal. High energy resolution of 29 - 48 meV and time resolution of 280 - 320 fs are demonstrated on 3D topological materials ZrTe$_5$ and Sb$_2$Te$_3$. Our work opens up new opportunities for exploring ultrafast dynamics in 3D quantum materials.