The structural, electronic, elastic, optical, phonon, and thermo-physical properties of the tetragonal X2CoH5 (X = Ca, Sr) hydrogen storage compounds were thoroughly examined using first-principles calculations. The negative formation enthalpies (−76.03 kJ/mol.H2 for Ca2CoH5 and −72.55 kJ/mol.H2 for Sr2CoH5) highlight the structural stability of these materials. Phonon calculations revealed no imaginary frequency modes, confirming the dynamic stability of X2CoH5. The mechanical stability of Ca2CoH5 and Sr2CoH5 was evidenced by the compliance of the elastic constants with Born stability criteria. The electronic band structure indicates that Ca2CoH5 and Sr2CoH5 are direct bandgap semiconductors with narrow bandgaps of ∼0.27 and 0.34 eV, respectively. The appraisal of Poisson’s ratio (ν = 0.22 for X = Ca and 0.23 for Sr) and Pugh’s ratio (B/G = 1.47 for X = Ca and 1.56 for Sr) suggests that both metal hydrides exhibit brittle mechanical behavior. Moreover, 3D plots of Young’s modulus (E), shear modulus (G), linear compressibility (β), and Poisson’s ratio (ν) uncover anisotropy within X2CoH5. The hydrogen storage capabilities were scrutinized, and the present materials feature excellent volumetric hydrogen density (95.65 gH2l−1 for Ca2CoH5 and 80.24 gH2l−1 for Sr2CoH5), moderate gravimetric hydrogen density (3.38 wt% for Ca2CoH5 and 2.06 wt% for Sr2CoH5) and high hydrogen desorption temperature (584 K for Ca2CoH5 and 558 K for Sr2CoH5). Notably, the obtained volumetric hydrogen densities are in line with the volumetric capacity criteria set by the U.S. Department of Energy (DOE) for 2025. Finally, the optical and thermo-physical characteristics of X2CoH5 compounds were also investigated in this work.