The atomic structure, electronic structure, and physical properties of (TiZrNbCu)1−xNix (x ≤ 0.5) metallic glasses (MGs) were studied in both the high-entropy (0 < x < 0.35) and the higher Ni concentration range (x ≥ 0.35). Atomic structure studies performed with X-ray diffraction and synchrotron powder diffraction provided average atomic volumes, structure factors, radial distribution functions, coordination numbers, and packing densities. Electronic structure studies performed using photoemission spectroscopy and low-temperature specific heat provided information about the electronic density of states within the valence band and at the Fermi level and also about interatomic bonding and atomic vibrations [from the Debye temperature and the boson peak (BP)]. Variations of both atomic structure and electronic structure with x showed a clear change for x ≥ 0.35, which corresponds to a valence electron number ≥7.4. All physical properties, namely, thermal stability parameters, Debye temperatures, BPs, magnetic, elastic, and electronic transport properties, change their concentration-dependence for x ≥ 0.35. The results are compared with those for binary and ternary MGs of the same elements.