Five Ir–Rh–Ru–W–Mo alloys selected based on alloy design with valence electron concentration (VEC) were examined for their formation of single, dual, and triple phases of bcc, fcc, and hcp structures. These structures were predicted with Thermo-Calc 2019a and the TCHEA3 database on a cross-sectional phase diagram along a composition line: Ir0.415254(100−2x)Rh0.415254(100−2x)Ru0.169492(100−2x)WxMox (x: 0–50 at%). At T = 2100 K, four types of phases were predicted: (1) a single bcc, fcc, and hcp phase, respectively, at x = 35 (Alloy A, VEC = 6.849), 15 (Alloy C, VEC = 7.981), and 5 (Alloy E, VEC = 8.574); (2) a mixture of bcc+hcp and hcp+fcc at x = 24 (Alloy B, VEC = 7.472) and 8 (Alloy D, VEC = 8.378), respectively; (3) a triple mixture of bcc+hcp+fcc; and (4) a mixture of bcc+fcc in Alloys A–E at low temperature. Experiments at 2100 K revealed that Alloys C–E tended to exhibit better reproducibility and that Alloy E can be regarded as a new refractory high-entropy alloy (HEA) with fcc structure. Alloy C annealed at T = 1273 K for 200 h maintained a single-hcp structure. The non-appearance of thermodynamically stable phases at low temperature in the Ir–Rh–Ru–W–Mo system was analogically explained as slow diffusion. The VEC analysis for HEAs with hcp structures was extended by including the range of 7.5 ≤ VEC ≤ 8.4 for alloys consisting of 4d and 5d transition metals annealed near their solidus temperature. The Ir–Rh–Ru–W–Mo system was significant in providing all possible simple solid solutions of bcc, hcp, and fcc phases.