How does C25k actually take you fromtimedrunning to running, er,5k?
The purpose of the program is to teach you to run for 30 minutes, not 5K. It's just "Couch to 30 min run" doesn't have the same ring to it.
There are C25K Plus podcasts on the NHS website. There are three, I'd recommend them as your initial post-C25K plan. These introduce the idea of monitoring your pace, running small sections at a faster pace (this is called "interval running") and there is also a coached 35 minute run.
When I graduated C25K I was covering 4km jn the 30m run. With 0.5km during the warm up and cool down walks, I was doing 5K over the whole of the session, but not at running pace. My first 5K all at a running pace took 42 minutes. But my second took under 40 minutes and it took maybe 4 or 5 runs to have a time under 35 minutes.
To make the swap, get an app that will tell you when you have run set distances. The fitbit app for example will tell you (via headphones or speaker) every 0.5km distance covered. Use at the same time as the C25K or C25K+ podcasts so you get a feel for the distances you are covering.
Then when doing your normal run, you may well find your pace/speed naturally improves as you repeat more often - so you'll cover a greater distance when running for the same amount of time.
Then some days maybe you'll feel good about your run and decide to keep going until you get the next distance marker - so run through the cool down.
I am not a social runner. I like the solitude of running alone and so Park Runs are not for me. Many new runners find them motivating though. I had a 5.5K route that I used all the way through C25K, but over time I ran more of it and walked less of it. Now I run 5k in about 30m and walk the last half km as a cool down. Door to door in 35 minutes. I do that every day. Some days adding in longer runs - I did a 10 miles/ 16km run the other week. Or 10k runs a couple of times a week.
You don't have to move to running according to distance. You could aim for a 35m run, then aim for a 40m run. Then aim for a 30+15 minute run (with a 5m walk break after half an hour). Then a 30+30 run with a short walk break. Then a 30+30+15 - you'll probably be around 10km at that point. But focus instead on how long you run for, not how far.