We develop a machine learning assisted workflow for the rapid screening of permanent magnet candidates within the CaCu₅ structure family. We generated more than 60,000 structures through substitutions. These compositions were screened using a combination of pretrained materials models, Materials Project data, and a machine-learning model for magnetization prediction. Four criteria, namely, metallicity, negative formation energy, energy above the convex hull ≤ 50~meV/atom, and predicted magnetization above the adopted ≥ 0.75~T threshold reduced the initial chemical space to 439 candidates for first-principles calculations. Density functional theory calculations revealed that 159 compounds exhibit positive axial magnetic anisotropy energy, favoring [001] over the tested in-plane directions. The resulting dataset reveals chemical trends in magnetic anisotropy across the CaCu₅ compositional space and provides a set of candidates for further investigation. More broadly, this work demonstrates a practical strategy for combining existing machine learning models with first-principles calculations to systematically reduce large chemical spaces to tractable sets for computationally intensive materials screening.