High pressure promotes the formation of polyhydrides with unusually high hydrogen-tometal ratios. These polyhydrides have complex hydrogenic sublattices. We synthesized iron pentahydride (FeH₅) by a direct reaction between iron and H₂ above 130 gigapascals in a laser-heated diamond anvil cell. FeH₅ exhibits a structure built of atomic hydrogen only. It consists of intercalated layers of quasicubic FeH₃ units and four-plane slabs of thin atomic hydrogen. The distribution of the valence electron density indicates a bonding between hydrogen and iron atoms but none between hydrogen atoms, presenting a two-dimensional metallic character. The discovery of FeH₅ suggests a low-pressure path to make materials that approach bulk dense atomic hydrogen.