This proposal plans to investigate the destruction of superconductivity by inter-band scattering in Lu_2Fe_3Si_5 doped by Y and Dy. Recent muon spin rotation studies have shown that Lu_2Fe_3Si_5 is multi-band superconductor. The introduction of non-magnetic impurities on the Lu site causes a rapid decrease of Tc in Lu_2Fe_3Si_5 This reduction is of a similar magnitude to that found for magnetic doping. We consider that this might be due to inter-band scattering, and eventually, when the concentration of impurities is large enough, the two gaps which dominate the properties of the pure compound will merge into a single gap.