The question is whether Disney needs to make a bigger offer before the Fox board meets. I'm not quite sure they have to and think it works out like this (as per the Variety article):
It sounds like after the Fox board determines Comcast made a higher offer, then the 5 day period matching period starts.
So this may stretch out another week.
Fox board meets Wednesday, and then Disney has until the following Wednesday, June 27, to match (i.e. 12 days from now).