A friend of mine pushed me into signing up for a 5k in early October. I'm 5'10" and 185lbs - a total lardfat.
I did a time trial in 27mins yesterday and can run 12 miles non-stop at an 11:00min/mile pace.
Can I shave 2 minutes of the 5k time with two weeks of intense training + 1 week taper, and losing 5lbs as well?
once you drop the 5 lb. if you do so gradually. you will likely notice no difference in speed at all. if you do so quickly. you will likely get a little slower.
3 weeks is a hell of a commitment. you might sign up for another 5k two months from your original fun run and enjoy the process slightly more.
the primary thing you might hope to gain in 3 weeks is enough interest to try a longer season. your 12 mile pace is nearly irrelevant for your current goal. what is your current time for 1.5 miles?
Week 1: 2 - 2 - 3 - 2 - 2 - 3 - rest
Week 2: 3 - 2 - 3 (a little bit faster than other days) - 2 - 4 - rest
Week 3: 2 - 3 (a little bit faster) -2 - 2 - 1 - 5K - rest and think about continuing the progression so you're in shape for next time
If your knees start hurting at any point, take a day or two off.
Yes, you can definitely shave 2 minutes off of 27 minutes in 3 weeks. This is how I used to train for a 5k that I ran each year way back before I actually started running. I probably went from ~24 to ~21 each year by running a few days a week for 3-4 weeks beforehand. Running a little bit regularly even for a short time drastically helps.
Do this:
Run 3-4 miles every other day at a relatively difficult effort.
Don't run at all in the 2-3 days before the race.
I bet you run a 24-25 minute 5k this way.
Honestly I wouldn't listen to any of this advice. I get that you want to make gains but 3 weeks isn't a lot of time. It takes time to progress in running and you're better off with long term goals. If you really want to drop a few minutes, run every day, push your body, and it might work out. You probably won't find much enjoyment.
I would think about lining up a 5k around Thanksgiving time since there are plenty of races. Train for 8-12 weeks. Build your mileage slowly. Add in faster running. Increase your long run. Pepper in plenty of easy days. Start that kind of training now & you'll get better for the 5k that's coming up but you won't burn out and will make bigger gains later.