Interdiffusion studies in Co-Cr-Fe-Mn-Ni, Co-Fe-Mn-Ni, Co-Cr-Fe-Ni, and Co-Cr-Mn-Ni, as well as a reevaluation of the previous results obtained for Al-Co-Cr-Fe-Ni, were conducted. In the experimental part, diffusion couples were annealed at four different temperatures: 1230, 1270, 1310 and 1350 K for each system. Then, the results were evaluated with use of the optimization-based technique, combined with the Miedema's thermodynamic description, what allowed obtaining of tracer diffusion coefficients for all elements in all considered systems. The correctness of the applied approach was tested on the example of Co-Cr-Fe-Mn-Ni system, showing very good agreement of determined tracer diffusivities with the values obtained by other authors. Obtained values of diffusivities were compared with the available data for a number of conventional binary and ternary systems. No signs of diffusion retardation were observed in the absolute temperature scale. In the case of temperature scale normalized with respect to the melting point, an abnormal behavior, previously attributed to the HEAs' sluggish diffusion effect was observed. However, it occurred only for alloys with prominent manganese content and was completely independent of the number of components, being just as likely to occur in binary systems as in HEAs. Therefore, the alleged sluggishness of diffusion in HEAs should be treated just as a result of specific compositions of the previously studied alloys and cannot be generalized for all high entropy systems.