In the UK 157,287 runners completed the latest Parkrun - a free timed 5km race that takes place in parks around the country (and increasingly around the world) each weekend.
The prevalence of Parkrun makes it an extremely accessible race distance and one worth focussing your training effort upon.
Regardless of your target time, training for a 5km race relies upon the same concepts - running fast and consistently. If you have never run before 'fast' might mean jogging around the course at a pace of 20 minutes per mile. Meanwhile an elite athlete may be targeting 5 minutes per mile.
If this is your first foray into running you will want to focus on simply getting out the door and gradually increasing your time on your feet.
Coach to 5k is a great place to start.
The Run48 mobile app offers a number of beginner level 5k training programs like this one from the team at CoolRunning.com.
To increase your speed your training should logically involve lots of running fast be it around a running track, on the road, or up (and down) hills.
To keep things interesting I would always recommend doing a variety of different runs or simply changing the interval distance. For example one week you might choose to run 4 x 400 metre intervals, whilst the next week you might choose to run 8 x 200 metres. Each interval of the former will be at a slower speed than the latter but the different training stimuli will result in different adaptations.
Hill runs are intervals in disguise. When running uphill you will find yourself running slower than when you run the same distance on the track but you will be recruiting a different set of muscles and will build up additional strength in your legs. If the race you are running has a hilly profile it is certainly worth adding in hill workouts to your training. As with normal intervals you can mix things up by running short, fast hills one week followed by longer, slower hills the next.
A lot of runners find that whilst training for longer race distances (like the marathon) that their 5k times also improve. This is because most longer distance training plans require lots of time on your feet and often times include speed work (like intervals and hill workouts). These training stimuli trigger adaptations.
Whilst 5k is significantly less than the 42km of the marathon it is still a significant distance (especially for new runners). It follows that if you have a lot of experience running 42km then running 5km will seem less significant - your body will have made endurance specific adaptations.
If you run fast every day, your body will not have sufficient time to recover. You will soon discover that you can not run fast anymore. For this reason most 5k training programs mix in harder speed sessions with longer endurance based sessions at an easier pace. The idea is that you can get time on your feet and practice running fast whilst allowing your body to appropriately recover.