The standard LCDM model has long served as a successful concordance model, reconciling the majority of cosmological observations. However, the era of "precision cosmology" has recently unveiled significant discrepancies, most notably the Hubble Tension and the debate over the dynamic nature of Dark Energy. This presentation suggests that the field is shifting from merely refining known parameters to searching for "new physics" through unexpected phenomena. We explore the synergistic research cycle between extragalactic observations and cosmological simulations. A primary focus is the Horizon Run 5 (HR5), a massive cosmological hydrodynamic simulation designed to capture both large-scale power and small-scale physics with high resolution. We compare HR5 predictions with recent high-redshift (z >= 5) galaxy stellar mass functions derived from JWST observations, discussing current agreements and discrepancies, particularly the underestimation of massive galaxy populations at 5< z <8. Furthermore, the presentation addresses the "Missing LSBG problem" and the study of Low Surface Brightness Galaxies (LSBGs) and IntraCluster Light (ICL) as key tracers for the mass-assembly history of galaxies and dark matter distribution in clusters. Finally, we introduce the DARWIN (DAzzling Realization of dWarf galaxies In the Next generation) project, a Korean consortium initiative aimed at resolving small-scale $\Lambda$CDM tensions and understanding the origin of dwarf galaxies through next-generation high-resolution simulations.