In our study, the composition-dependent effects of atomic displacements in Au-Cu-Ni-Pd-Pt based alloys, comprising elements with large differences in atomic radii, are investigated at the atomic scale. Two alloys—the equimolar AuCuNiPdPt and AuCuNiPd—have been characterized using multi-edge extended X-ray absorption fine structure (EXAFS) spectroscopy in conjunction with reverse Monte Carlo (RMC) simulations at room temperature. The statistically-averaged component-dependent pair distribution functions (PDFs), which represent the distribution of atoms around the assumed regular face-centered cubic (fcc) lattice positions, reveal a shift of their peaks to shorter distances and a pronounced asymmetry in atomic distribution only for atoms with small radii (Cu/Ni). The analysis demonstrates that small atoms (Cu/Ni) are significantly more displaced from the expected lattice positions as compared to large atoms (Au/Pt). Furthermore, there are indications of preferential next-neighbour bonding that changes depending on the alloy composition. The most pronounced changes in the PDFs were found solely for Pd. With this study, we provide a basis for a deeper understanding of the composition-dependent atomic arrangement in chemically complex solid solutions.