Due to the rising demand and carcinogenic effect of cobalt, alternative metal matrixes need to be developed for hot-pressed diamond tools. Due to this reason High-Entropy alloys without cobalt were calculated via phase fraction diagrams. Three alloys of the Al–Cu–Fe–Mn–Ni system Al30Cu30Fe5Mn25Ni10, Al11.25Cu35Fe5Mn20Ni28.75 and Al5Cu20Fe25Mn25Ni25 were chosen due to their different crystal structures ranging from pure bcc, eutectic fcc-bcc to pure fcc crystal structure. Cr5Cu20Fe25Mn25Ni25 was chosen to verify the change of one element on the consolidation properties. The alloys were mechanically alloyed and hot-pressed at 800 °C for 3 min without and at 900 °C for 3 min with diamonds. Porosity increased with the fraction of bcc solid solution in the investigated alloys of the Al–Cu–Fe–Mn–Ni system. Samples consisting of Cr5Cu20Fe25Mn25Ni25 showed the lowest porosity, which was attributed to precipitation of a second copper-rich fcc solid solution around the remaining pores. At a process temperature of 800 °C and 3 min isothermal hold the samples featured a porosity of only 2.72%. Within the XRD patterns and SEM images of the hot-pressed samples with diamonds no graphitization or formation of carbides could be observed. Therefore, Cr5Cu20Fe25Mn25Ni25 was identified as a promising cobalt free metal-matrix candidate for diamond tools.