The compound, Tb5Si3, crystallizing in Mn5Si3-type hexagonal structure, was recently reported by us to exhibit a sudden and huge enhancement in electrical resistivity (rho) at a critical magnetic field (H_cr) in the magnetically ordered state (<70 K) tracking isothermal magnetization (M) behavior. We have investigated the influence of external pressure (<15 kbar) and negative chemical pressure induced by Ge substitution for Si on M and rho as a function of temperature (5-300 K) and magnetic field (<120 kOe), with the primary aim of understanding the field-induced anomalies. Focussing on isothermal M and magnetoresistance (MR) at two temperatures, 5 and 20K, we find that this rho anomaly persists under external as well as negative chemical pressures, however with a large change in the H_cr. The pressure-derivative of H_cr is negative and this trend and the MR behavior at the H_cr are comparable to that observed in some Laves phase itinerant magnetic systems. On the basis of this observation, we speculate that the magnetic fluctuations induced at this critical field could be responsible for the MR anomal.ies