Created one of the first and studied more than 20 years ago, high-entropy five-component alloys CoCrFeNiMn (Cantor alloy) and CoCrFeNiAl still attract the attention of researchers in the field of physical materials science due to their possible application in various industries because of their successful combination of strength and plastic properties. To date, a large amount of experimental materials has been accumulated on the ways to control the properties of these alloys. This article reviews the publications of domestic and foreign authors in two areas of improving the properties of these alloys: alloying, precipitation and heat treatment, and the use of CALPHAD phase diagrams. In the first direction, the role of alloying with B, Al, V, Si, Nb is analyzed; γ and γ′ nanoprecipitations, various modes of thermal and deformation processing. It was concluded that it is necessary to conduct experiments on the alloying of HEAs with Zr and Nb, which have proven themselves well in hardening steels. Creation and modification of the properties of five-component HEAs is possible using the CALPHAD computer programs developed for calculating state diagrams. The results of publications on the thermodynamic description of five-component alloys analyzed in the article are confirmed by comparing the phase diagrams with the available experimental data. In one of the analyzed works on the phase formation of five-component HEAs consisting of Co, Cr, Fe, Ni, Al, Mn, Cu, 2436 compositions were considered, which made it possible to determine 1761 variants of reliable prediction of the formation of bcc/B2 and fcc phases, bypassing amorphous phases and intermetallic compounds, thereby designing a certain level of mechanical properties. It is shown that the design of a new generation of HEAs is possible based on calculation of the CALPHAD phase diagrams.