I'm following the same plan, albeit quite loosely. I'm in my 7th week, I found the first 2 or 3 weeks a struggle and didn't feel any improvement. However during that third week I did one longer run that wasn't on the plan just to see how I coped and after 1.5 miles I just felt a bit of a second wind and managed to complete 5k but with 3-4 walking breaks. It was overdoing it to be strict but I had no adverse symptoms from doing so. From then on I tweaked the plan and basically increased the running element by about a minute every second run and recently I decreased the walking interval to just 1 minute. Yesterday I did my run as 3 x 9 min runs and 1 mins walking. Today I got my new trainers and being anxious to try them out I went for another run. Normally I'd run every second day. Anyway I decided to just do 1 interval of running for as long as comfortable and I managed a 21:43 / 2.47 mile in one go which I was incredibly pleased and surprised with. I did it as a test of how far I've come in 7 weeks, the early weeks I could run no more than 4/5 minutes without walking for a minute or two. On my next run I'll go back on plan and run 10-12 min intervals with 1 min walks so I can continue to build my fitness gradually. Today was literally a test.
In my opinion, and I'm no expert at this, in 3 weeks or so you may feel a marked difference. I certainly did and for the next few runs I actually overdid it. I'm now expecting to be able to run 30 mins in 2 weeks or so which I already know for my average speed is over 5K.
I'm 36, haven't exercised in 15 years or so and I'm average weight and spot on BMI. You have youth on your side, if I can do it then you certainly can.
Stick with it, tweak it a little if you feel you need to and I'm certain you'll do that 5k run in one go. Good luck.
Edited: 03/05/2012 at 22:25