Undoubtedly the invention of multi-principal- component or high-entropy alloys (MCAs or HEAs) is a milestone in the historical development of alloys since they provide large degrees of freedom in alloy designs and applications. Enthalpy is by no means the only decisive factor for alloy forming; entropy is yet another important factor due to the existence of multi-principal- component. Viewing their 'equal' effect on alloys, it is necessary to consider both of them in researching properties of HEAs. To elucidate their influence on alloys, we design an experiment to investigate how microstructure of six five-component equi-atomic HEAs of a constant configuration entropy, Rln5, changes with different mixing enthalpies, i.e., with different combinations of components from the single set of (Al, Co, Cr, Fe, Ni, Ti). Totally six different phases comprising pseudo-A1, -A2, and -A3 solid solutions, and A12, D0 24 , and L2 1 intermetallic compounds that are formed during solidification and during homogenization afterwards are found in the system. Whether a phase is a solid solution or an intermetallic compound has been examined by a mixing entropy-enthalpy plane (referred as MEE plane). In the plane, the negative sign branch of the two critical phase boundary lines that satisfy the critical condition of ±ΔH = TΔS separates a solid solution state from an intermetallic state. This plane may be a convenient substitute in analysing HEAs rather than the complex hyper-dimensional phase diagram needed conventionally. In all the designed alloys, each of them possesses at most three phases indicating that there are at least four degrees of freedom in the alloys by an argument of the Gibbs phase rule. The new occurrence of an L2 1 -multi- component Heusler phase always results from the coexistence of both Al and Ti components in the alloys. A schematic compositional relationship diagram of related alloys in references is also given in this study.