The playoff roster is just a subset of your major league roster (which itself is a subset of your 40 man roster).
As long as the R5 player remains on your ML roster, you are good. This implies that he does NOT need to be on your playoff roster.
Though I believe he loses his R5 status once the regular season has concluded, and can be treated as a "regular" player after that point.
ML service time does not get counted beyond the end of the regular season, so playoff time does not earn service time.