High-entropy alloys (HEAs) are a new class of materials with an attractive combination of tunable mechanical and physicochemical properties. They crystallize mainly in cubic structures, however, for practical applications, HEAs with hexagonal-close-packed (hcp) structure are highly desirable in connection with their, in general, high hardness. Herein, we report the synthesis, structure, and detailed superconducting properties of Re0.56Nb0.11Ti0.11Zr0.11Hf0.11 -the first hexagonal superconducting HEA composed of five randomly distributed transition metals. A combination of room-temperature precession electron diffraction, precession electron diffraction tomography, and powder x-ray diffraction is utilized to determine the room-temperature crystal structure. Transport, magnetic, and heat capacity measurements show that the material is a type-II superconductor with the bulk superconducting transition at T-c = 4.4 K, lower critical field H-c1 (0) = 2.3 mT, and upper critical field H-c2 (0) = 3.6 T. Low-temperature specific-heat measurement indicates that Re(0.)(56)Nb(0.11)Ti(0)(.11)Zr(0.11)Hf(0)(.11 )is a phonon-mediated superconductor in the weak electron-phonon coupling limit with a normalized specific-heat jump Delta C-el/gamma nT(c)= 1.32. Further, hexagonal to cubic structural transition is observed by lowering the valence electron counts and T-c follows crystallinelike behavior.