Polycrystalline Ba6Mn5O16 has been characterized by neutron diffraction and magnetic measurements. The structural essential feature of Ba6Mn5O16 is the presence of zigzag layers perpendicular to [010] separated by Ba atoms and folded along the c axis. The layers are built up from (Mn5O18) units constituted by five face-sharing octahedra connected via their apices by two of their three terminal corners at each end of the (Mn5O18) group. The Ba6Mn5O16 magnetic structure, determined from the neutron diffraction data, suggests a strong antiferromagnetic coupling within the (Mn5O18) units, and also an antiferromagnetic coupling between the different layers along [010]. Ba6Mn5O16 presents a long-range three-dimensional antiferromagnetic order below TN=87K. Around this temperature, the specific heat is comparable to that shown by Ba4Mn3O10, the difference being related to the different number of the magnetic atoms in each case. From the magnetic specific heat, the value of the entropy associated with the antiferromagnetic ordering is obtained for both layered phases.