I would say go for it, but between now and then increase your running distance slightly.
If you run the same distance every time you go out your body will just get used to running that distance and you won't progress, also you'll probably end up finding it tedious and when the weather turns bad your motivation won't be there so much.
Maybe on your next run you could run a little further to about 3 and a half. Next week try running a 4 mile run on one of the days you go out.
The important thing is to increase your distance very gradually and if you need to, do the extra bit at a slightly slower pace.
You've got 17 days until the 10k, try and get up to one run of 5 miles before then.
Another way of increasing strength and fitness is hill training. If possible you could dedicate one of your sessions to hill training. Find a hill of a decent distance, and after warming up, run up the hill and then jog down to recover. Do as many reps of the hill as you can but depending on your fitness already, you could start with 4 or 5.
Good luck with the 5k this weekend
