<human>: (FYI, I'm 36 y/o, female, and slightly overweight but quite strong)

So I'm week 8 of the C25K and LOVING IT and I know I don't want to stop at 5k. I've already got my eye on an 8k in October, and a 10k in April -- and I don't just want to finish those, I want to finish them at a speed of 11km/hr or faster. (it's a long story)

Right now I'm averaging 8.5-9km/hr on a hilly course. I know I need to increase my distance and my speed, and my plan is to work up to doing 1 long run per week, some speedwork, race pace runs, 'easy runs' etc.

The only thing I'm struggling with is frequency. A lot of what I have been reading suggests that you need to be running 5-6 days per week, and then a lot of other sources suggest 3 days per week is sufficient. So which is it?

For the last few weeks I've been running 4-5 days per week, and at 5 days per week I seem to be sustaining some damage to my calves/lower tendons. I know I need to get hardened to running, and I thought that the way to do that was to just run more often... so I'm feeling a bit frustrated today as I missed this morning's run because my calves were sore enough that I knew I would injure myself.

I am being pretty careful about form when I am running, including keeping my strides straight and long, using a mid-sole strike, and keeping my abs and lower back engaged. With every run my form feels better and more smooth. 

Recovery wise, I have a regular yoga practice, and on top of that I stretch my "problem areas" (hip flexors, calves and pecs) three times per day as per the instructions of an RMT that I have worked with for other sports. Before a run I warm up but don't stretch, and I do stretch after a run, as well as first thing in the morning and evening.

Give me the gist of the text in a nutshell
<bot>: How many days per week should I be running if I want to build up my speed and endurance to be able to run a 10k in 55 minutes?