So you're running 5k = 3 miles three times a week and have four weeks to your 10k.
My suggestion would be to increase one of your training runs to 4 miles this week, then next week increase one to 5 miles; then reduce your miles to 2 or 3 on your training runs, giving yourself a good rest before your 10k.
I'm no expert, but that sounds manageable, and if you can run 5miles in training you'll have no real problems with a 10k.