Occasionally the running bug bites. It's certainly not something everyone experiences, but for those who do experience it, they'll need to train properly in order to have a long running "career". Proper progressions are the best way to build up your distance and pace.
Your 5K is done and passed and now you're working toward double that distance; a 10K. Most people who have run a 5K can very likely go outside right now and run a 10K. It may be painful, slow, and exhausting, but they can probably do it. Sometimes the goal is just to do it as Nike would say. But if you're looking to do it well, there are a few things you should do.
1: Foam rolling just became extremely important to you.
Longer distance running will put stress on your body. Obviously your lower body specifically, but your upper body as well. Foam rolling will help remove knots and break up scar tissue in the muscle which allows for a proper range of motion. It also helps improve blood flow to the muscle.
2: Begin by adding a longer run to your week.
The first thing most people will do (if they are following a progression) would be to slightly increase the length of all of their runs from week to week. While that will help you to reach your goal, there is a better way. If you are doing three runs per week (Monday, Wednesday, Friday) and you're just beginning your program to reach your 10K, consider your Monday being 3.3 miles, Wednesday at 3.7 miles, and Friday at 3.5 miles. That's opposed to a strict progression where you just run 3.3, 3.3, 3.3 for the week and take it higher the next week. Following the first progression you'll reach your goal faster and get practice pushing yourself just a LITTLE further than you think you can go.
3: Develop a post-run stretching routine and never break it.
After your run you will have some tightened muscles. If not properly stretched these muscles can become injured. Tight muscles can also lead to limited ranges of motion which often lead to compensations and injuries as well. Maintaining a proper stretching routine will keep your muscles healthy and help keep your range of motion in line.
I hope these strategies help you build up to your first 10K. There is a lot more to consider when training (rest, hydration, time, intensity, which stretches, etc.) but if you begin incorporating our three suggestions you'll be well on your way.