For the first time in the literature, experimental determination of entire sets of exact interdiffusion coefficients in quaternary and quinary alloy systems is reported. Using the method of body-diagonal diffusion couple, a set of nine quaternary interdiffusion coefficients were evaluated in Fe–Ni–Co–Cr and a set of sixteen quinary interdiffusion coefficients were determined in a Fe–Ni–Co–Cr–Mn system, both at approximately equimolar compositions. Regions of uphill interdiffusion and zero flux planes were observed for nickel and cobalt in quinary couples, indicating the existence of strong diffusional interactions in Fe–Ni–Co–Cr–Mn alloys. The strong diffusional interactions were also manifested in the large magnitudes of cross coefficients in both the systems. The existence of strong diffusional interactions in high-entropy alloys (HEAs) as observed through experimentally determined interdiffusion coefficients in this study establishes beyond doubt the fact that cross interdiffusion coefficients cannot be ignored in HEAs.