If I run 5 miles a day at roughly 8 minutes per mile, am I decently prepared for boot camp?
That's a pretty decent start. Maybe work on getting your speed up though? I had a way of increasing speed and distance that worked wonders for me, and I can share that here. I can't speak to the rigors of boot camp, however. You may also want to add some weight training for extra insurance.
What I did was to first, aim for a certain distance. I ran every other day, but each time I was able to add distance. Then when I reached a new distance (let's start with your 5 miles), then I would work on speed but stay at that one distance. So it would take you 40 minutes to run 5 miles (after properly warming up). Try to do it in 35 minutes. (Again, rest a day in between.) You might decrease time slowly; 38, 37, 36 minutes...but eventually you will hit your 35-minute mark. Then aim for 30 minutes - or get as close to that as you possibly can, slowly, steadily. Then, when you make the time, increase your distance again!
I used that technique and it worked incredibly well for me. I was very happy with the results. I was running 7 miles in about 40 -45 minutes. I loved it! Felt like a warm-up too, not even a workout!
Not sure how much time you have before you start bootcamp, but if you have the time you might want to try it. Just remember to eat healthy, drink enough water, and get enough sleep too.
Good luck - best wishes at bootcamp! :-)