Magnetic, specific heat, and structural properties of the equiatomic Cantor alloy system are reported for temperatures between 5 K and 300 K, and up to fields of 70 kOe. Magnetization measurements performed on as-cast, annealed, and cold-worked samples reveal a strong processing history dependence and that high-temperature annealing after cold-working does not restore the alloy to a "pristine" state. Measurements on known precipitates show that the two transitions, detected at 43 K and 85 K, are intrinsic to the Cantor alloy and not the result of an impurity phase. Experimental and ab initio density functional theory (DFT) computational results suggest that these transitions are a weak ferrimagnetic transition and a spin-glass-like transition, respectively, and magnetic and specific heat measurements provide evidence of significant Stoner enhancement and electron-electron interactions within the material.