The results of two experiments designed to synthesize element 115 isotopes in the 243Am+48Ca reaction are presented. Two new elements with atomic numbers 113 and 115 were observed for the first time. With 248-MeV 48Ca projectiles, we observed three similar decay chains consisting of five consecutive α decays, all detected in a total time interval of 30 s. Each chain was terminated by a spontaneous fission (SF) with a high-energy release and a lifetime of about a day. With 253-MeV 48Ca projectiles, we registered a different decay chain of consecutive α decays detected in a time interval of 0.5 s, also terminated by spontaneous fission, but after 1.8 h. The decay properties of the eleven new α- and SF-decaying nuclei are consistent with expectations for consecutive α decays originating from the parent isotopes 288115 and 287115, produced in the 3n- and 4n-evaporation channels, respectively. Support for the assignment of the atomic numbers of all of the nuclei in the 288115 decay chain was obtained in an independent experiment in which a long-lived spontaneous fission activity, 268Db (15 events), was found to be chemically consistent with the fifth group of the periodic table. The odd-odd isotope 288115 was observed with largest cross section of about 4 pb. In the SF decay of 268Db, a total kinetic energy of 230 MeV and a neutron multiplicity per fission of 4.2 were measured. The decay properties of the 11 new isotopes with Z=105 115 and the production cross sections are in agreement with modern concepts of the role of nuclear shells in the stability of superheavy nuclei. The experiments were carried out at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research.