AgentGinger wrote (see)
initially i could not complete 5k without having to slow to a brisk walk. my breathing has improved and i can cover ~10 miles in about 1:30:00 without stopping, and my 5k and 10k paces are slowly improving, but I'm not really pushing myself, so I feel like now I can start to test my speed.
That's some serious progress - well done!

As for improving your times, simply going out and running will improve your race times naturally, simply through your heart being able to utilize oxygen better. However, if you want to get good improvements (and over a shorter time period as well), then - like you said - doing some speedwork sessions and tempo runs will knock some serious time off.
In terms of speedwork, try something like this: Find a 400m running track (or a 0.25 mile stretch of quiet road - the distances are roughly the same) and run the 400m at your goal 5k race pace. Jog slowly back to the start and repeat 8 - 10 times.
For 10k, I have found that running 1600m on a track (which is a mile, give or take) at your goal 10k race pace, with 400m jogs recoveries, about 4 - 6 times is a good session.
A tempo run, once a week, will probably see the biggest benefit in your 10k time. Run at a pace that is about 15-30 seconds per mile slower than your goal race pace, for about 20 minutes to begin with, gradually adding on time each week.
These sessions tended to work for me, although I haven't done any 5k - specific speedwork in a while, so chances are there are better programmes out there than the ones I mentioned above.
Edited: 08/10/2009 at 16:31