High-entropy alloys are random alloys with five or more components, often near equi-composition, that often exhibit excellent mechanical properties. Guiding the design of new materials across the wide composition space requires an ability to compute necessary underlying material parameters via ab initio methods. Here, density functional theory is used to compute the elemental misfit volumes, alloy lattice constant, elastic constants, and stable stacking fault energy in the fcc noble metal RhIrPdPtNiCu. These properties are then used in a recent theory for the temperature and strain-rate dependent yield strength. The parameter-free prediction of 583 MPa is in excellent agreement with the measured value of 527 MPa. This quantitative connection between alloy composition and yield strength, without any experimental input, motivates this general density functional theory-based methodological path for exploring new potential high-strength high-entropy alloys, in this and other alloy classes, with the chemical accuracy of first-principles methods.