I took up BJJ (individual rather than team sport) as a way to fill my evenings, and to try to get back into martial arts. I've taken up a strength training (bodyweight) as a way to improve myself there.
The exercise isn't always fun, but it has a purpose beyond "run faster" or "lift more" (though those are fine goals as well, just insufficient motivators for me).
Congrats. I'm still a white belt and will probably remain one. They go to a gym up in Atlanta when they want to test and award belts, on a Saturday, and it almost always coincides with a soccer game. Priorities. :)
A major part of long distance running (10k+) is the mental aspect.
You are never, ever, going to get the mental endurance and discipline to run fast for distance by running for a short period of time, no matter how hard.
I think many people could easily train to do 5k and then 10k and get many benefits. Our very evolution came about from persistence hunting which means many people should have the genetics for endurance and far fewer for intensity (speed).