We have calculated the five-loop RG expansions of the n-component A model of critical dynamics in dimensions d=4−ɛ within the Minimal Subtraction scheme. This is made possible by using the advanced diagram reduction method and the Sector Decomposition technique adapted to the problems of critical dynamics. The ɛ expansions for the critical dynamic exponent z for an arbitrary value of the order parameter dimension n are derived. Based on these series, the numerical estimates of z for different universality classes are extracted and compared with the results obtained within different theoretical and experimental methods.