Make running a family event. Present it as something you can do together. Make it a fun activity that offers its own rewards.
Conversely, if your kids are old enough, encourage them to do some training on their own. They’ll value their independence and might more grown up if their parents aren’t always involved. If they have friends who are also training, they can run together.
Figure out what motivates your kids. Some are competitive, others not. Some will get deeply involved in preparation, as if it’s a science project, others just want the experience. Some like to push themselves, others just want to feel good in the moment.
They should have good quality running shoes that fit well. Ideally, their shoes and their other running clothes should also look good—in their eyes, not yours. Don’t underestimate how motivating it is for kids to be happy with their style.
Make sure your kids eat enough, and especially make sure they drink enough. Risk being overbearing on these points. Life lessons such as “drink before you’re thirsty,” “go to the bathroom before it’s an emergency,” and “dehydration makes you feel like death” are hard-won. Kids won’t be quick to take your word for it.
There’s plenty of flexibility with a 5K. How far in advance your kids start training really should depend on their current level of fitness. A couple of months should be plenty even for relatively sedentary kids. Start them off with a couple of runs a week. They can be short. And if running feels too hard, encourage them to run for a couple of minutes, walk for a couple, then repeat for twenty minutes or so.
Gradually work up to longer runs and more days per week. There’s no need for them to run more than four days a week, unless they really want to. A couple of rest days should be mandatory. They can do anything they want on a rest day, as long as it doesn’t involve running.
Don’t make every training day the same. A typical week could have one longish day (which by the end can be as long as 4K or so), one or two medium days, and one short and fast day. The fast day can be structured as sprints separated by walking or slow running, or as longer intervals. If you have kids who are training together and are competitive, you can encourage them to race each other.
Be flexible and creative. If your kid seems overly tired, or bored, find a way to change things up. Keep it interesting and motivating.