The current study presents the results from the experimental research conducted on the influence of the regime parameters on the process for a five-dimensional Ball Burnishing (BB) finishing process with the help of a CNC milling machine on the Regular Reliefs (RR) obtained on complex functional surfaces. The elements of the technological system, necessary for the formation of RR of type IV on the complex surfaces, are presented. A planned factorial experiment is realized, through which the significantly affecting parameters of the BB process on the size and shape of the RR cells, are determined. The results obtained are statistically confirmed by a dispersion analysis (ANOVA) carried out. Conclusions, regarding the possibilities of obtaining RRs of type IV on complex surfaces through a process of five-axis simultaneous BB, are made