Step one to finishing a 5K or a faster 5K has nothing to do with running.
I firmly believe that before you ask your body to do anything--whether it's lugging around a carseat carrier with a 10-pound bundle of joy or running a 5K--your body has to be strong enough for the task.
I'd say the majority of moms aren't strong enough for the daily grind of motherhood. That's why our backs hurt, our knees give out, or other strains and pains come out of nowhere. What's more, to stay ahead of the curve, we have to be able to lift, squat, carry, or otherwise move around the weight of our heaviest child. As a mom, you HAVE to get stronger as your kids get older. But, what typically happens is as the kids grow up and get busier, mom does less and less for her strength and health.
Then she decides she's going to get fit again and out the door she goes for a run. Disaster waits.
Two to three times a week I work on building strength, with butt-building lifts like squats (which as we know by now does double duty strengthening the pelvic floor to prevent a leaky bladder), spine cinching lifts like deadlifts, and upper body work like push press, pull ups and push ups. Sometimes I use kettlebells, sometimes barbells, sometimes dumbbells, sometimes my own bodyweight. I make it hard for myself. And in one of those workouts I include some sort of plyometrics: box jumps, squat jumps, broad jumps, jumping lunges. When I am ultra sore, the ploymetrics are to blame, but those exercises are like the booster rockets to your training.
Stronger muscles are less likely to get injured. Stronger muscles work more efficiently. And the fringe benefit of efficiency is speed.
If you don't know where to start, look back at my Training for Motherhood Workout Instruction Video and my Training for Motherhood With Kids Video. If you're fresh out of childbirth, start with Sahrmann exercises. Look into bootcamp at your fitness center. Go find a Cross Fit gym. Find workouts online. They are everywhere. Heck, today I did a "deck of cards" workout. Pick an exercise to represent the suit on the cards, then draw cards and do the the number of reps on the card: face cards=10 and aces=11. Make the joker something really hard. Do as many cards as you can in 10 minutes, 20 minutes, or whatever time you have. Is there an app for that? Yes, there is.
Just get stronger. It will help whether you're running toward a finish line or chasing after your children.