High-entropy alloys (HEAs) have gained considerable attention from the scientific community over the last decade due to their remarkably adjustable mechanical properties (high hardness, high elevated-temperature strength, high fatigue resistance, good oxidation resistance and good age-softening resistance) arising from the unique compositions and micro/nanostructures. HEAs composed of elements with high melting temperatures, for instance refractory metals, would be potentially suitable for applications at high temperatures and pressures, and minimize costs. Mo-Nb-Ta-V-W based HEA that forms a single-phase BCC-structure with density of 12.2g/cc has shown notable mechanical strength up to operational temperatures of ~1600°C. Here we present results of our computational investigation on tailoring the alloy chemistry of Mo-Nb-Ta-V-W HEAs to obtain targeted properties at elevated temperatures. We establish a fundamental knowledge base on the phase equilibria of these material systems that is vital for understanding the formation of solid solution phases, microscopic structure and improving mechanical properties.