Systematic theoretical results for La(TM)₅Hₙ materials with TM one of the magnetic transition metals Fe, Co, or Ni are discussed. For TM = Co, Ni the antecedent LaCo₅ and LaNi₅ intermetallics and hydrides are well known. While no La–Fe compounds exist, LaFe₅ hydrides are predicted to form by both Miedema's phenomenological model as well as by first-principles density functional theory (DFT) for several prototype crystal structures. Enthalpies of formation and saturation hydrogen contents derived from Miedema's model and DFT are compared. Our phonon calculations for LaCo₅ and LaCo₅H₄ yield new information on their crystal structures.