A beam of MeV protons, accelerated by ultraintense laser-pulse interactions with a thin target foil, is used to investigate nuclear reactions of interest for spallation physics. The laser-generated proton beam is shown (protons were measured) to have a broad energy distribution, which closely resembles the expected energy spectrum of evaporative protons (below 50 MeV) produced in GeV-proton-induced spallation reactions. The protons are used to quantify the distribution of residual radioisotopes produced in a representative spallation target (Pb), and the results are compared with calculated predictions based on spectra modeled with nuclear Monte Carlo codes. Laser-plasma particle accelerators are shown to provide data relevant to the design and development of accelerator driven systems.