All papers have been peer-reviewed. The 5th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2007), Official Conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), and the 5th International Conference on Computational Methods in Sciences and Engineering 2007 (ICCMSE 2007), Recognized Conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE) have both taken place at Hotel Marbella in Corfu, Greece between 16th and 20th September 2007 and 25th and 30th September 2007, respectively. We note that for ICCMSE there is a co-sponsorship by American Chemical Society. The aim of ICNAAM is to bring together leading scientists of the international Numerical and Applied Mathematics community and to attract original research papers of very high quality. The ICCMSE is unique in its kind. It regroups original contributions from all fields of the traditional Sciences, Mathematics, Physics, Chemistry, Biology, Medicine and all branches of Engineering. It would be perhaps more appropriate to define the ICCMSE as a Conference on Computational Science and its applications to Science and Engineering. Based on the universality of mathematical reasoning the ICCMSE favors the interaction of various fields of Knowledge to the benefit of all. Emphasis is given to the multidisciplinary character of the Conference. The principal ambition of the ICCSME is to promote the exchange of novel ideas through the close interaction of research groups from all Sciences and Engineering. In this Volume, we present special contributions of these two Conferences which cover the aim and the scope of each of these events.