Over 20 new compounds of the RE6T5Al7 series (RE = Sc, Y, Ce-Nd, Sm, Gd-Lu; T = Ru, Ir; Yb6Ir5Ga7 type structure; superstructure of MgZn2; fully ordered Nb6.4Ir4Al7.6 type) have been synthesized. They crystallize in the hexagonal crystal system with space group P6(3)/mcm. Their lattice parameters are in the ranges of a = 935-963 and c = 851-874 pm for the RE6Ru5Al7 and a = 913-966 and c = 825-865 pm for the RE6Ir5Al7 series. Four structures (Ho6Ru5Al7, Yb6Ru4.68(1)Al7.32(1), Sc6Ir5Al7, and Ho6Ir4.53(1)Al7.47(1)) have been refined from single-crystal data, indicating fully ordered structures for Ho6Ru5Al7 and Sc6Ir5Al7; however, T/Al mixing was observed on one crystallographic site for Ho6Ir4.53(1)Al7.47(1) and on two sites for Yb6Ru4.68(1)Al7.32(1). The Sc-, Y-, and Lu-containing compounds exhibit Pauli paramagnetism in line with a filled d band for Ru and Ir. Ce6Ru5Al7 exhibits mixed-valent behavior, while Yb6Ru5Al7 is solely trivalent. The other compounds exhibit paramagnetism and ferromagnetic phase transitions up to temperatures of T-C = 83.4(1) K for Gd6Ru5Al7. In addition to the basic magnetic characterizations and studies of the electrical resistivity and heat capacity, the magnetocaloric properties of Gd6Ru5Al7, Tb6Ru5Al7, and Dy6Ru5Al7 have been investigated, revealing magnetic entropy changes of -Delta S-M(max) = 6.2(1), 7.7(1), and 5.4(1) J kg(-1) K-1 (0 -> 5 T) and relative cooling powers RCP = 242, 207, and 135 J kg(-1), respectively. For a deeper insight into the second-order magnetic phase transitions, the critical behavior was investigated according to the scaling hypothesis. The critical behavior of Gd6Ru5Al7 is in accordance with the mean-field theory; the critical exponents of Tb6Ru5Al7 and Dy6Ru5Al7, however, deviate strongly from this universality class. For comparison of the structural and magnetic properties, the thus far unstudied members of the RERuAl series (RE = Sc, Y, Sm, Gd-Lu; MgZn2 type) have additionally been prepared and characterized.