I would try and run to see how long I can run and start from that week, instead of going from the beginning of C25K, since you have already done it couple of years ago. Saying that, if you have not done any running for the last one year or so, you will find it harder so it is only you now from where you should start. Don't worry about speeding up for the moment. Once you are able to run a 5K, then as crox says, do one slow but longer run and 2 faster runs, ie 2 runs of 5K and one of 10K a week, it helps, that is how I could speed up.There are good runs and bad runs along the way though, as you know, but you just have to keep going. Good luck!
Intervals work well for increasing speed. But do it gradually. Replace one run a week with an interval session:
Warm up, easy jog, flat out can't breathe going to die sprint for 30 seconds, recover, repeat however many times you can manage (four is good), cool down.
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