Neutron powder diffraction on the binary intermetallics Er5Mg24 and Tm5Mg24 confirms their isostructural and pure crystallization in the Ti5Re24-type structure (space group I (4) over bar 3m, Z = 2) with rare earths located in 2a(0,0,0) and 8c(x,x,x) and Mg in two different 24g(x,y,x) sites. Room temperature lattice constants are 11.263(2) Angstrom and 11.215(1) Angstrom for the Er and Tm compound, respectively. Atomic positions have been refined. Both compounds order ferromagnetically below Curie temperatures of 17.5(5) K and 7.5(5) K for Er5Mg24 and Tm5Mg24, respectively. The magnitudes of the Er moments at 4.2 K are 7.5(2) mu(B) and 4.4(2) mu(B) on the 2a and the 8c sites, respectively. The Tin moments which have been refined from 2 K measurements amount to 3.0(3) mu(B) and 2.8(2) mu(B), respectively. The temperature dependencies of the magnetic Bragg intensities reveal distinct deviations from Brillouin curves for J = 15/2 (Er) and J = 6 (Tm) systems and indicate a complex magnetic exchange.