To expand further on both of our posts...
5th starter will need to make 8 starts pre- ASB
there's 77 games after the ASB, with only 4 off days. Skipping the 5th whenever possible makes 13, 12 if you pitch someone on 3 days rest to end the season. 15 would be the most likely scenario, with a top of the rotation type of guy, and every one pitching an equal # of games.
So from june 12th- October 3rd, the sox will need between 20 and 23 starts out of the 5th starter. Rain outs/double headers could call for more starts.