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In this work, we consider the spherically symmetric black hole solution of the Randall-Sundrum (RS) model. This asymptotically-Schwarzschild solution was recently found by Abdolrahimi et al. (ACPY-solution). We investigate the specific properties of the accretion disk around astrophysical black holes described by the ACPY-solution thus considering the possibility of observational testing the RS model. The energy flux and temperature distribution are obtained and compared to the Schwarzschild solution. We present the spectral energy distribution of the accretion disk around RS black holes. A precise determination X-ray observations of their thermal spectrum might allow to identify deviations of gravity from Relativity (GR). We use recent data on the high-mass X-ray binary Cygnus X-1 and on the Galactic centre black hole candidate Sgr A* to analyze the values of the parameters of RS model.