We have measured the electrical resistance of micrometric to nanometric powders of the La_5/8-yPr_yCa_3/8MnO₃ (LPCMO with y=0.3) manganite for hydrostatic pressures up to 4 kbar. By applying different final thermal treatments to samples synthesized by a microwave assisted denitration process, we obtained two particular grain characteristic dimensions (40 nm and 1000 nm) which allowed us to analyze the grain size sensitivity of the electrical conduction properties of both the metal electrode interface with manganite (Pt/LPCMO) and the intrinsic intergranular interfaces formed by the LPCMO powder, conglomerate under the only effect of external pressure. We also analyzed the effects of pressure on the phase diagram of these powders. Our results indicate that different magnetic phases coexist at low temperatures and that the electrical transport properties are related to the intrinsic interfaces, as we observe evidences of a granular behavior and an electronic transport dominated by the Space Charge limited Current mechanism.