sc42 did you run across the country several years back?
There is NO doubt during his racing season he will run 4 miles on grass at 5:40. So we want to get him ready for it.
The first thing we suggested was fartlek on grass. Has the OP even run on grass all summer? This should be his hard workout. One minute on one or even two minutes off that will help him the most. Aim to do more repeats (limit 20 then cut rest from say 2 minutes to 1:45)rather than run the minutes faster.
His second workout can be a tempo this workout shouldn't be hard it should just get him doing something he doesn't normally do. Running 6 or 7 miles at 6:30 pace would be a great first tempo workout. 7 days later trying 5 at 6:15 even better.
It is better to go into practice ready to try to run 4 miles at 5:40 when the coach asks for it rather than have tried it 4 times and only successfully completed the workout once.