If you can already run 5k, there is no point in doing the c25k program.  Instead, look for a 5k racing training program.  Usually that involves adding more interval sessions, and tempo runs.  Mix up your training, so that you do some days slow and long and some days with high speed intervals. 

I'd be slightly cautious on one thing:  I believe many of the programs that focus on improving time (speed) come with them an inherent assumption that the runner has been running for a while and has a base of miles established.  You said you *can* run 5K, but have you been doing so consistently?  If you don't consider yourself a consistent runner then, IMHO, I would first establish a routine where you're running that 5K 3-4x/wk.  Do that for a number of weeks to establish a base.  Get all parts of your body used to the routine.  Routines like C25K help you ease into running not only because of the fitness needed, but there is a lot of adjusting and getting your body accustomed to the rigors of running that needs to take place.  I've seen lots of stories of people who are very active (bikers, swimmers, etc.) who can handle the fitness side of running very quickly, but they'll get some other sort of injury because their feet or ankles or knees or leg muscles aren't used to that particular activity.  I've even heard the bone density changes as you run more and more consistently.  So if you get into it too quickly it's easier to get a stress fracture.

So if you don't have a consistent base - I'd focus on that.  THEN look at a program to increase speed.  Right now - I wouldn't worry too much about the technique and science.  That is a whole 'nother program that may come up as you focus more on speed.

Good luck.

Jim

I agree that a C25K really isn't the place to foster a goal of 5K in 18min and you really should have some kind of 'speed' coach to help you get faster and not get injured doing it.  A mix of base 3mil runs with core workout, intervals and a 'long' once a week should get you there.  Just to relate to what you are doing,  I recently added my 'long' of 4 miles to my weekly routine and brough my speed from 10.5 down to 9.5.  I know doesn't sound like much but for me it was a huge improvement and I felt great after the 3 mile run.  Looking forward to an 8.5 in another month.

You can definitely do sub 6 min miles if you build slowly up to it.  Please post your progress here and what training you are doing to help you get there.

I would be careful not to try and beat your 5K time everytime you go out.  Your daily runs should be done at different tempos/paces and you shouldn't be "racing" everytime.  I would do 1 time trial a week where you really go for it.  Maybe even every other week.