Well you can't do the same thing all the time and expect a different result meaning you need to change things around a bit and spend some time outside your comfort zone.
Most of us try to avoid speed work because it hurts and for the first timer it might not be as enjoyable as it feels like you're starting from the beginning all over again.
This is when you need to be patient as the gains will come quickly and speed work will not only make you faster but it will also improve your fitness. But you can't just do speed work! To avoid injury you need to have already built up a good aerobic base and ideally have completed the race distance you want to improve on. Think of the aerobic base as the foundation on which to build further fitness.
For the beginner, Hills are a great way to start speed work. You might not feel like you're running fast but the increased effort to work against gravity will improve your strength for the forward motion.
6* 1 minute uphill with a gentle jog or walk back down for recovery. Increase by 1 rep per week up to 10 reps. This session will be as hard as you want it to be and to begin with you take it easy and remember how far a minute takes up and you can compare it as the weeks go by.
Another session that's easy to try is the fartlek. This comes from the Swedish term for speed play and it's basically an unstructured speed session and you just do what you can for as long as you can. You decide on the time, distance and pace for your fast running but don't overdo it.
After 2K of easy running pick a point in the distance which could be a lamppost and run at a pace that you can sustain until you get to it. You then take as much time as needed to recover and repeat until you want to cool down. Intervals can be as long or as short as you want. If running with a friend you can add a bit of uncertainty into the mix by taking turns at deciding the distance and pace for reps.
For a more structured interval session you choose a set distance and pace or for the beginner it can be time and pace.
After your warm up run for 6*1 minutes at your target race pace with I minute jog recovery. As an example, if your 5K best time is 30 mins and you want to target 25 mins then you would run at 5 min per K pace for 1 minute with 1 minute recovery and repeat for 6. To work out pace you should ideally use a GPS watch / smartphone app or if you have access to a running track then you can work out your time per 100M to check your pace. For this example 100M should be covered in 30 seconds and your 1 minute interval should equal 200M.
As it becomes more manageable you can increase the length of the intervals until you can run for 5 mins. Do remember that when you increase the working time then you must also increase the recovery time.
Do not run faster than you need to and only do enough to achieve your goal.
For the first few sessions be cautious and introduce yourself rather than jump straight in as you don't want the first session to be your last. I see this quite regularly and unless you have a coach to guide you then you'll need to be patient to begin.