You are looking for something beyond just starting up.
A 5km race is a great way to focus on speed training and building speed even for longer runs
A 10km race is a great way to push yourself to the max as you build endurance while staying focused on maintaining as close to your 5km race speed. This is perhaps one of the toughest distances to race.
For the long distance runner in you, late Spring and Summer is a good time to focus on doing a great 5 or a 10k race.