Ternary hexagonal Ae(5)Tt(3)Z phases have been obtained from high-temperature reactions (1000-1300 degreesC in Ta) only for Ae (alkaline-earth metal) = Ca, Tt (tetrel) = Pb, and Z = V, Cr, Mn, Fe, Co, Ni, Zn, Ru, or Cd. The hexagonal crystal structures (stuffed Mn5Si3-type, P6(3)/mcm, Z = 2) were refined for Z = Mn and Fe (a = 9.3580(3), 9.3554(5) Angstrom, c = 7.009(1), 7.009(1) Angstrom, respectively). In contrast, Ca(5)Pb(3)Z for Z = Cu or Ag form only with a trigonal structure (P (3) over bar c1, Z = 2, a = 9.4130(3) Angstrom, c = 7.052(1) Angstrom for Cu) in which regular displacements of only the linear strings of Ca1 atoms occur. The existence of these compounds stands in contrast to the nonexistence of all binary Ae(5)Tt(3) products from Ca to Ba (Ae) and Si to Pb (Tt) with a Mn5Si3-type structure. Therefore, it once seemed attractive to consider the Z elements in these Ca(5)Pb(3)Z compounds as reducing agents (electron donors). The Mn and Fe structures appropriately exhibit greatly enlarged antiprismatic calcium cavities about Z. Other indications of relatively electron-poor environments around Fe are found in its properties, which include soft ferromagnetism with an elevated magnetic moment (6.3 mu(B)) and a large Fe 3p(3/2) binding energy relative to that in La5Ge3Fe, La15Ge9Fe, etc. The Ca5Pb3Mn phase exhibits metallic behavior (rho(295) = 135 muOmega cm) and temperature-independent Pauli paramagnetism. These properties are supported by ab initio band structure calculations for Ca5Pb3Mn, which show strong Ca-Pb bonding and a broad Pb-based band, with appreciable Ca-Mn and Ca-Pb bonding states at and above E-F. Distortion of the Cu analogue gives strengthened Ca-Pb bonding and reduced Cu-Ca1 repulsions. A Zintl phase description of these compounds and some releated compounds in terms of closed Pb bands is not appropriate.