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High-entropy alloys (HEAs) have emerged as favorable choices for different applications, including superconductors. The present work examines the impact of nanostructuring via high-pressure torsion (HPT) on the superconducting properties of the equiatomic TiZrHfNbTa HEA. Structural characterization reveals a progressive refinement of grain size and increased dislocation density, together with partial phase transformation to an {\omega} phase with HPT processing. Magnetic susceptibility and magnetization measurements indicate a systematic enhancement in the superconducting transition temperature (from $T_c =$ 6.2 K to 7.2 K) and critical magnetic field, as well as the stabilization of the superconductivity state by HPT processing. The improvement of superconducting properties is attributed to microstructural modifications such as grain boundary density, defect generation and phase transformations, and their impact on vortex pinning, quantum confinement and electron scattering. The results suggest that nanostructuring through severe plastic deformation provides an appropriate route to optimize superconducting properties in high-entropy superconductors.