  A theoretical model for two new tellurite-sulfates, namely
Na$_2$Cu$_5$(TeO$_3$)(SO$_4$)$_3$(OH)$_4$ and K$_2$Cu$_5$(TeO$_3$)(SO$_4$)$_3$
(OH)$_4$ is determined to be compatible with ab-initio calculations. The
results obtained in this work show that some previous speculations in the
literature about the couplings are correct, obtaining a model with a mixture of
ferromagnetic and antiferromagnetic couplings. We use a combination of
numerical techniques to study the magnetic properties of the model. Our
numerical calculations based on the density-matrix renormalization group method
reveal that the system presents Ising-like magnetization plateaux at rational
values of the saturation magnetization.
