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High-entropy alloys (HEAs) are a class of multi-element materials that exhibit unique structural and functional properties. This study reports on the synthesis and characterization of a superconducting HEA, (NbTa)0.55(HfTiZr)0.45 fabricated using the vacuum arc melting technique. Scanning electron microscopy and energy-dispersive x-ray spectroscopy were employed to analyze the material's morphology and composition. X-ray diffraction analysis revealed a single-phase body-centered cubic (BCC) structure with a measured nanoindentation hardness of 6.4 GPa and Young's modulus of 132 GPa. This HEA superconductor was investigated by x-ray diffraction at Beamline 13BM-C, Advanced Photon Source, and the BCC phase was stable to the highest pressure of 50 GPa. Superconductivity was characterized by four-probe resistivity measurements in a quantum design physical property measurement system, yielding a superconducting transition temperature (Tc) of 7.2 K at ambient pressure and reaching a maximum of 10.1 K at the highest applied pressure of 23.6 GPa. The combination of high structural stability enhanced superconducting performance under pressure and superior mechanical properties highlights (NbTa)0.55(HfTiZr)0.45 as a promising superconductor under extreme environments.