The two volume-set, LNCS 7930 and LNCS 7931, constitutes the refereed proceedings of the 5th International Work-Conference on the Interplay between Natural and Artificial Computation, IWINAC 2013, held in Mallorca, Spain, in June 2013. The 92 revised full papers presented in LNCS 7930 and LNCS 7931 were carefully reviewed and selected from numerous submissions. The first part, LNCS 7930, entitled "Natural and Artificial Models in Computation and Biology", includes all the contributions mainly related to the methodological, conceptual, formal, and experimental developments in the fields of neurophysiology and cognitive science. The second part, LNCS 7931, entitled "Natural and Artificial Computation in Engineering and Medical Applications", contains the papers related to bioinspired programming strategies and all the contributions related to the computational solutions to engineering problems in different application domains, specially Health applications, including the CYTED "Artificial and Natural Computation for Health" (CANS) research network papers. In addition, this two volume-set reflects six interesting areas: cognitive robotics; natural computing; wetware computation; quality of life technologies; biomedical and industrial perception applications; and Web intelligence and neuroscience.