Great. That 4 miler. It's really good to have at least half a mile at a gentler pace than going 100%! And if you're ever doing a serious attempt at a 5K time trial/park run, it will make quite a difference to jog a mile first, then do some hundred+ metre runs approaching race-pace to get all those physiological systems turning over.
There's obviously some simplifications in there.... but hopefully helpful to get you to the next stage, and get you reading more about the subject.
Good luck with those knees. Get good shoes. Run on softer surfaces when possible... and work out if tennis is damaging your knees. If so, think about taking some tough decisions. If they're getting knackered already... a lot of your life is spent over the age of 40 and you don't want to be restricted.
Where I said do tempo runs one week and intervals the next, I would really focus more on tempo type runs 2 weeks in every 3.
Interval training is done at faster speeds. This definitely has its place and is good for you, but given where you are, I would have a bias towards doing aerobic and tempo runs.
Also, to be clear, when you run your 5K race (which I'm assuming is your short/mid term focus), most of your energy comes from the aerobic system... so the more efficient you can make that system, the better. But you do dip into those anaerobic systems, with the nasty biproducts... so you do benefit from that speed work.
18:30 is pretty impressive given your background. Surely tennis is hard on those knees... maybe time to drop it and become a runner
I'd make the following observations
You've done a 3.1 mile park run at sub 6 minute pace, but you say that 4 miles at 6:30 pace was challenging (you couldn't maintain it for 10km.
This is a clear indicator that your aerobic base is weak. (when your run 'aerobically' you are running at a pace where you create almost all of your energy by burning fuel (usually glycogen from carbohydrates) using oxygen that you breathe in
This is exactly what you must expect on your training and tennis background. To improve, you need to exercise aerobically for longer periods. I would build that long run up to at least an hour and on one of your rest days, could you fit in another aerobic exercise without knackering your knees? Swim? Cycle? It could make a really very big difference if you can only run twice a week. (would be good for your tennis too)
When you are racing a 10K or shorter distances, you go at speeds that need more energy than can be supplied just by burning glycogen with the oxygen you breathe. The aerobic system still plays an important part, but other energy systems come into play - which are essentially anaerobic - fuel sources are broken down by enzymes for fast release of energy. The downside of these processes are that they produce waste products that can and do slow you down once they build up.
Your slow runs train your aerobic energy systems. But you should do one 'speed' session a week. Mix it up a bit. Maybe 800m or 1200m intervals one week, tempo the next. Tempo runs are good (make sure you do at least a mile, preferably 2 warming up and building speed before the speedy bits. Find good speeds for training here www.runnersworld.co.uk/general/rws-training-pace-calculator/1676.html
Running your tempo runs at around 10K pace is done for 2 reasons. Partly so you aren't cream crackered for your next session/tennis match but importantly, it ensures you recruit and train the optimum anaerobic energy systems.
In simple terms your aerobic runs increase the pace you can run before your body needs to recruit anaerobic systems - so it is a pace that can be maintained for a long time, as few nasty waste products build up in your blood/muscles.
And your tempo runs do produce waste products - but you run them at a pace where your body is at a threshold and can just about clear that waste at a rate that stops them building up too much. If you run that tempo run too fast (say at 3K race pace), then your system will get flooded by waste products, you'll get knackered quickly, and there isn't an optimum training effect (you really want to work on increasing that "threshold" pace - above which waste products start to build rapidly. Running for 20-40 minutes at your current threshold pace (approx 10-14K pace) will help increase your threshold pace.
So I would strongly recommend that you don't do a Park Run or 2 mile time trial every week. Do your park run once a month to monitor progress and have fun, but you'll get much better training effect by running a bit slower (maybe 6:20 pace) for a bit longer).