The high-entropy transition metal borides containing a random distribution of five or more constituent metallic elements offer novel opportunities in designing materials that show crystalline phase stability, high strength, and thermal oxidation resistance under extreme conditions. We present a comprehensive theoretical and experimental investigation of prototypical high-entropy boride (HEB) materials such as (Hf, Mo, Nb, Ta, Ti)B2 and (Hf, Mo, Nb, Ta, Zr)B2 under extreme environments of pressures and temperatures. The theoretical tools include modeling elastic properties by special quasi-random structures that predict a bulk modulus of 288 GPa and a shear modulus of 215 GPa at ambient conditions. HEB samples were synthesized under high pressures and high temperatures and studied to 9.5 GPa and 2273 K in a large-volume pressure cell. The thermal equation of state measurement yielded a bulk modulus of 276 GPa, in excellent agreement with theory. The measured compressive yield strength by radial X-ray diffraction technique in a diamond anvil cell was 28 GPa at a pressure of 65 GPa, which is a significant fraction of the shear modulus at high pressures. The high compressive strength and phase stability of this material under high pressures and high temperatures make it an ideal candidate for application as a structural material in nuclear and aerospace fields.