High-entropy alloys are currently considered as prospective hydrogen storage materials and getters, which can be utilized to create a high vacuum in specialized devices. To provide high sorption properties, it is crucial to use highly porous materials or powders that makes powder metallurgy an attractive and suitable method. In the current work, a powder high-entropy alloy TiZrHfNbTa was obtained by reducing transition metal oxides with calcium hydride. The mechanism and features of the calcium-hydride synthesis of the high-entropy alloy have been studied. Phase composition has shown to be dependent on holding time at a temperature of 1200 °C. The powder’s structure comprises four BCC solutions based on Nb, Ta, TiZrHf, and TiZrHfNb, when holding time is up to two hours. Prolonged holding leads to more homogeneous structure, and the final product possesses two BCC phases: Ti0.21Zr0.24Hf0.24Nb0.25Ta0.06 (BCC-I: ∼75 wt%) and Ti0.15Zr0.05Hf0.08Nb0.10Ta0.62 (BCC-II: ∼25 wt%). The analysis of BCC-I formation kinetics with the aid of the Avrami equation has shown that a quite prolonged time of around 48 hours is necessary to achieve a single-phase structure of the powder due to the presence of tantalum, which impedes homogenization. Parameter n in the Avrami equation has been determined to be 0.361.