Delve into the fifth lecture of the "Introduction to Numerical Relativistic Hydrodynamics" series, presented by Kenta Kiuchi from the Albert Einstein Institute. Explore advanced concepts in numerical relativity and hydrodynamics as part of the Summer School on Gravitational-Wave Astronomy. Gain insights into solving field equations of General Relativity in conjunction with magnetohydrodynamics equations using supercomputers. Understand the crucial role of numerical simulations in accurately modeling mergers of black holes or neutron stars, massive star collapses, and accreting black holes. Learn about the significance of these simulations in interpreting gravitational-wave signals and multi-messenger observations. Discover how this field contributes to our understanding of high-energy astrophysical phenomena targeted by upcoming gravitational-wave, electromagnetic, and neutrino observatories.