  In this report, a successful thermodynamical model was employed to understand
the structural transition in Er$_5$Si$_4$, able to explain the decoupling of
the magnetic and structural transition. This was achieved by the DFT
calculations which were used to determine the energy differences at 0 K, using
a LSDA+U approximation. It was found that the M structure as the stable phase
at low temperatures as verified experimentally with a $\Delta F_0 = -$0.262 eV.
Finally, it was achieved a variation of Seebeck coefficient ($\sim$ 6 $\mu$V)
at the structural transition which allow to conclude that the electronic
entropy variation is negligible in the transition.
