I was in a similar spot a few years back. Drunkenly bet a buddy that I could still crack 5:00 in the mile, and agreed to go for it in a time trial about 6 weeks later. At the time I was in my late 20s, running maybe 3-4 times a week (~15-20mpw total), and my most recent race was a 1:28 half marathon. My best guess is that at the time of the bet I could have run in the 5:3x range. Cracking 5 would also put me pretty close to my PR (I never said I was fast), so this was a tall order.
I agree with the others who have said that you need to prioritize foot speed over endurance given the limited ramp time, but disagree with how best to do this. Unless your friend has been regularly running hard workouts, trying to hit the track and go hard 3x/week is a recipe for disaster. I'd take 2 easy days after every hard workout. Something like this:
M: Track workout (e.g. 10x300m, 2-4-6-8-6-4-200m pyramid, etc.). Shoot for 2-2.5 miles of hard work, avoid intervals longer than 800m
T: Easy
W: Easy + strides
Th: Moneghetti fartlek (great bang for your buck, good practice for running fast when tired)
F: Easy
Sat: "Long" (1 hour at most, very easy) + strides
Sun: Rest / crosstrain
A week out, run a 1000m time trial at goal pace. That will give you familiarity with the discomfort to expect, and hopefully also the confidence that you can push through that last lap and a half on game day.
For the record, I ran 73-75-78-72 and came through the line in 4:59.7. Best of luck!