<p>Lightweight Mg-containing high-entropy alloys (HEAs) hold significant application potential in structural lightweighting due to their low density and high specific strength. In this work, body-centered cubic (BCC) and face-centered cubic (FCC) structures of equiatomic five-element MgAlAgXY (<i>X</i> = Nd, Gd, Er; <i>Y</i> = Ca, Pb, Si, Sn, Zn) alloys are constructed using special quasi-random structures (SQS), and their formation enthalpies, densities, and elastic constants are calculated <i>via</i> first-principles to assess thermodynamic and mechanical stability. The calculations reveal that all MgAlAgXY alloys exhibit lower formation enthalpies than the experimentally reported Al₂₀Li₂₀Mg₁₀Sc₂₀Ti₃₀ HEA, demonstrating superior thermodynamic stability that depends significantly on alloy composition and crystal structure; among them, MgAlAgErSi, MgAlAgGdSi, and MgAlAgNdSn show the lowest formation enthalpies. Regarding mechanical properties, Er and Nd elements have a greater influence on the elastic modulus, all alloys display ductile characteristics, and the Si element exerts the most significant impact on overall mechanical properties. Comprehensive evaluation based on formation enthalpy, density, elastic moduli, B/G ratio, Poisson’s ratio, and hardness identifies MgAlAgErSi, MgAlAgGdSi, and MgAlAgNdSi as the most promising candidates with an excellent balance of low density, high thermodynamic stability, and superior mechanical performance. While the inclusion of Ag and rare earth elements increases material cost, and Pb raises toxicity concerns, the present computational framework enables efficient screening of cost-effective and environmentally friendly compositions in future studies.</p>