This study is the first to combine energetic neutral atom (ENA) observations from Two Wide‐Angle Imaging Neutral‐Atom Spectrometers (TWINS) and Interstellar Boundary Explorer (IBEX). Here we examine the arrival of an interplanetary shock and the subsequent geomagnetically effective substorm on 5 April 2010, which was associated with the Galaxy 15 communications satellite anomaly. IBEX shows sharply enhanced ENA emissions immediately upon compression of the dayside magnetosphere at 08:26:17+/−9 s UT. The compression drove a markedly different spectral shape for the dayside emissions, with a strong enhancement at energies >1 keV, which persisted for hours after the shock arrival, consistent with the higher solar wind speed, density, and dynamic pressure (∼10 nPa) after the shock. TWINS ENA observations indicate a slower response of the ring current and precipitation of ring current ions as low‐altitude emissions ∼15 min later, with the >50 keV ion precipitation leading the <10 keV precipitation by ∼20 min. These observations suggest internal magnetospheric processes are occurring after compression of the magnetosphere and before the ring current ions end up in the loss cone and precipitate into the ionosphere. We also compare MHD simulation results with both the TWINS and IBEX ENA observations; while the overall fluxes and distributions of emissions were generally similar, there were significant quantitative differences. Such differences emphasize the complexity of the magnetospheric system and importance of the global perspective for macroscopic magnetospheric studies. Finally, Appendix A documents important details of the TWINS data processing, including improved binning procedures, smoothing of images to a given level of statistical accuracy, and differential background subtraction.