To qualify for nuclear applications, materials must meet specific criteria, including mechanical properties, high-temperature behavior, corrosion resistance, and high-temperature oxidation resistance. High Entropy Alloys (HEAs) are particularly suitable for these applications due to their unique properties. Consequently, we conducted a theoretical and simulation-based approaches to assess some critical properties including radiation shielding properties of some quinary FeNiCoCr HEAs. In this study, we focused on quinary FeNiCoCr HEAs, whose corrosion properties have been previously examined in the literature. We investigated the thermodynamic and radiation shielding properties of HEAs with sixteen different compositions. Our methodology included evaluating thermodynamic parameters such as Mixing Entropy (∆Smix) and Mixing Enthalpy (∆Hmix), as well as structural characteristics like Valence Electron Concentration (VEC) and Atomic Size Difference (δ). This allowed us to systematically deduce the phase behavior and stability of various HEAs. Through computational modeling, we assessed the radiation shielding capabilities of these alloys, particularly their effectiveness in attenuating gamma ray and fast neutrons. The results identified FeNiCoCrW as the alloy with the lowest fast neutron removal cross-section values, highlighting its potential for nuclear applications. Its high melting point and the synergistic interplay between its elemental composition and thermodynamic properties suggest broad applicability in extreme environments. Thus, FeNiCoCrW emerges as a promising HEA with multifunctional capabilities, warranting further exploration and potential integration into advanced engineering solutions.