We successfully synthesized the ternary bismuthides La3MBi5 (M = Ti, Zr, Hf). These compounds crystallize in the hexagonal Hf5Sn3Cu-anti type structure (space group: P63/mcm) consisting of face-sharing MBi6 octahedral chains and hypervalent Bi linear chains, both separated by La atoms. Magnetic susceptibility and electrical resistivity measurements revealed that all of the compounds, including the solid solution La3Ti(Bi1-xSbx)5, exhibit a Pauli paramagnetic behavior without any trace of superconductivity down to 1.85 K, as opposed to a recently reported 4 K superconductivity in La3TiSb5. The absence of superconductivity is supported by first-principles band calculations of La3TiBi5 and La3TiSb5 that demonstrate similar electronic structures with three-dimensional Fermi surfaces.