This work is devoted to examine the galactic behavior of entropy by checking the validity of thermodynamics laws for the teleparallel reduction of Kaluza-Klein theory in thermal equilibrium state. We assume a flat Friedmann-Lemaitre-Robertson-Walker type space-time model in which dark matter is interacting with dark energy. With this scenario, calculating the variation of galactic entropy function for each dark components and for the dynamical apparent horizon itself, we prove that the thermodynamical laws are independent of the specific interaction term and dependent of the selected Kaluza-Klein model. Finally, some limiting conditions and their implications have been presented.