The current-voltage characteristics of -AgRbAg4I5C+ cell are measured and described in terms of a model assuming that the electron current across the electrochemical cell is essentially defined by the transfer of electrons through the interface. The position of the Fermi level in the band gap and the value of the electronic conductivity sigma(e) similar or equal to 2.5 x 10(-9) Omega(-1) cm(-1) are determined. The role of the near contact region and silver dendritic clusters in the process of electron transport in RbAg4I5 superionic crystals are studied. The onset of the exponential rise of the current at increasing voltage V (at V greater than or equal to 450 mV) is described within the model based on the conception that the silver dendritic clusters fractally grow at the interface. It is shown that the increase of the voltage leads to growth of the effective interface area (due to the cluster structure formation) and as a result to the exponential increase of the current through the cell at V greater than or equal to 450 mV. At constant voltage on the cell we observed experimentally the electronic current instability. We suppose that at this voltage some of the clusters reach the opposite electrode that leads to stochastic current oscillations. The number of these clusters increases with the voltage growth and therefore the current oscillations become more frequent. All experimental data are well described within the framework of the theory of reversible diffusion limited aggregation without branching.