High‐entropy alloys (HEAs) with face‐centered‐cubic (FCC) structures, e.g., the typical CrMnFeCoNi HEA, have a strong tendency to precipitate brittle sigma phases, as Cr is a strong sigma stabilizer. To develop HEAs with alleviated concerns of sigma phases, Cu for Cr in the Cr‐Mn‐Fe‐Co‐Ni HEA system is substituted to form a Mn‐Fe‐Co‐Ni‐Cu system. The quinary alloy and its quaternary subsets are investigated all in as‐cast state. Microstructure evolution, phase constituent, and tensile properties at room temperature are studied. The HEAs have multi‐phase FCC structures with slightly different lattice constants and spherical Cu‐rich particles are observed in most systems. All alloys exhibit dendrite‐like morphology with Cu segregation in interdendritic regions due to the solute partitioning. The investigated HEAs show good strengths, large elongations, and work hardening capability. The strengths are attributed to combined mechanisms, especially the precipitation strengthening by Cu‐rich particles. The findings provide some model HEA systems for further usefully guiding design in the widely compositional space of Cr‐free HEAs.