The 5 mwd is easy to counter.
1) Assure the players that there will be 6 to 8 encounters per day.
2) Random encounters will have a chance to occur after the first two short rests until the 6-8 encounters happened.
3) random encounters do not count toward the number of foes in an adventure, do not provide meaningful treasure and do not give any exp.
4) random encounters migjt, can and will provoke a TPK if players are out of resources.
5) some "adventure" fights are worth more than one encounters, random always count as one and only one encounter. No matter the difficulty.
At first, some players will balk at these notions. After a few games, they will get the picture and go for the attrition style of play. And after a campaign, they might not want to hear of any other type of campaign like my players do.