Measurements of the antinucleon-nuclei annihilation cross section (σ ann ) at very low energies have been performed at CERN during the 80's and 90's with the LEAR facility and more recently with the Antiproton Decelerator. One of the unexplained results is the behaviour of the antineutron data on several nuclei (C, Al, Cu, Ag, Sn, Pb) at momenta below 180 MeV/c [1], where the σ ann values, as a function of energy, have a steep rise typical of low-energy charged projectiles [2]. In order to put strong constraints on the relative strength of antineutron and antiproton interaction with nuclei, a comparison of σ ann for antiproton and antineutron projectiles with the same targets at the same energies is needed. To date this has been possible only for the hydrogen target (for momenta below 80 MeV/c) and for the tin target for which an antiproton measurement was performed at 100 MeV/c [3]. The ASACUSA Collaboration has recently performed the measurement of the σ ann of 5.3 MeV antiprotons on carbon. The preliminary result is here presented and the prospects are discussed.