Superconducting high-entropy alloys (HEAs) are a newly burgeoning field of unconventional superconductors and raise intriguing questions about the presence of superconductivity in highly disordered systems, which lack regular phonon modes. In our study, we have synthesized and investigated the superconducting characteristics of two new transition elements based HEAs Re$_{0.35} $Os$_{0.35} $Mo$_{0.08} $W$_{0.10} $Zr$_{0.12}$ (ReOMWZ) crystallizing in noncentrosymmetric $\alpha$-Mn structure, and Ru$_{0.35} $Os$_{0.35} $Mo$_{0.10} $W$_{0.10} $Zr$_{0.10}$ (RuOMWZ) crystallizing hexagonal closed-packed structure (hcp). Due to its high hardness, transition-metal-based hexagonal hcp HEA is rare and highly desirable for practical applications. Bulk magnetization, resistivity, and specific heat measurements confirmed bulk type-II superconductivity in both alloys. Specific heat analysis up to the measured low-temperature range suffices for a BCS explanation.