What weight training exercises can I do with dumbbells that will benefit me most for running 5-10ks? Are stomach crunches/sit ups worth doing too?
I'd recommend going with a rapid fire style of workout using light dumbbells that is a hybrid of both cardio and strength training. For instance, see this video from Scott Abel. The rationale for why you would want to do this workout is in the zentofitness.com article, too.
Your aim with weight training for running is for strength and not for "bulking up".
There are a whole bunch of exercises that you can find just by Googling "weight training for running".
With dumbbells you will be looking at doing things like lunges, steps and squats to target the legs.
Again, just Google "dumbell squats" etc. and have a look on youtube to see videos.
I also suggest doing crunches and sit-ups for long distance running. You will find that strong abdominals helps improve balance and if your legs are quite strong you will notice the burn in your abs once you start running long distances.
Running benefits from strength in the posterior chain, particularly the hamstrings, glutes, and lower back. Lower body strength generally will help as well. Dumbbell squats, squat-jumps, lunges, and deadlifts, done as heavy as possible, would be ideal for this goal.
Power and speed development is also important. For that purpose, dumbbell cleans, swings, and snatches are called for.
In the interest of balance, it might be nice--but not required--to add in some overhead presses and dumbbell rows for the upper body.
I don't see any particular reason to do sit-ups for a 10k race, particularly if you're getting stronger in the abs from heavy lifting. I prefer planks. But they would probably be fine.