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The primary motivation for the series of International Conference “Nuclear Theory in the Supercomputing Era (NTSE)” (http://ntse.khb.ru) was the rapid growth of supercomputers and the impact they, along with theoretical and algorithmic developments, are having on nuclear theory. The first conferences in this series, “Horizons of Innovative Theories, Experiments, and Supercomputing in Nuclear Physics” (HITES-2012) and NTSE-2012, were hosted respectively by the Louisiana State University in New Orleans, Louisiana, USA in June 4–7, 2012 (http://www.phys.lsu.edu/hites2012) and by the Pacific National University, Khabarovsk, Russia in June 18–22, 2012 (http://www.ntse-2012.khb.ru). These conferences were proceeded later under the common title NTSE. The NTSE-2013 (http://ntse.khb.ru/2013) was hosted by the Iowa State University, Ames, Iowa, USA in May 13–17, 2013 and celebrated the 70th birthday of Professor James Vary. The NTSE-2014 (http://www.ntse-2014.khb.ru) was hosted by the Pacific National University, Khabarovsk, Russia in June 23–27, 2014. These proceedings includes talks presented at the NTSE-2016 Conference hosted by the Pacific National University, Khabarovsk, Russia in September 19–23, 2016. The Conference was sponsored by the Pacific National University, Khabarovsk, Russia and by the Russian Foundation for Basic Research.