Herein we report the first high-pressure study of the energetic material 3,4,5-trinitro-1H-pyrazole (3,4,5-TNP) using neutron powder diffraction and single-crystal X-ray diffraction. A new high-pressure phase, termed Form II, was first identified through a substantial change in the neutron powder diffraction patterns recorded over the range 4.6-5.3 GPa, and was characterised further by compression of a single crystal to 5.3 GPa in a diamond-anvil cell using X-ray diffraction. 3,4,5-TNP was found to be sensitive to initiation under pressure, as demonstrated by its unexpected and violent decomposition at elevated pressures in successive powder diffraction experiments. Initiation coincided with the sluggish phase transition from Form I to Form II. Using a vibrational up-pumping model, its increased sensitivity under pressure can be explained by pressure-induced mode hardening. These findings have potential implications for the safe handling of 3,4,5-TNP, on the basis that shock- or pressure-loading may lead to significantly increased sensitivity to initiation.