High entropy superalloys (HESA) are promising materials with unique properties, but their development and optimization remain ongoing. This study focuses on Fe-based HESA FeNiCrAlCu and their stacking fault energy (SFE), a critical parameter influencing deformation mechanisms and creep resistance. Leveraging machine learning and computational thermodynamics, we propose a novel approach for predicting SFE using big data analysis. However, thermodynamic data of some rare elements like Zr is limited. Then, we use first-principles to investigate further the effect of adding Zr on elastic properties, SFE, and electronic structure. Our research establishes an optimal design guide for achieving desired SFE values: Ni (20-25 at%), Cr (15-36 at%), Al (5-20 at%), and Cu (9-20 at%). We achieve an impressive 0.98 accuracy in classifying SFE types by employing a deep learning neural network model. This work advances HESA design, provides valuable insights into their mechanical behavior, and improves creep resistance for demanding applications.