A warm up is important for quality training runs, even if it’s not that long (mine isn’t). I’ll do a few resistance band exercises for my hips and glutes, jog half a mile, then do 4 or 5 dynamic stretches. It’s not a precise routine, but the habit is important.
For my cool down, I’ll jog another half mile, and then start on recovery fuel and do some crunches. Then I’ll do a stretch routine that takes about 15 minutes. Each pose I hold for 30 seconds.
Post-run stretching is important for me. Even if it’s only 10 minutes, I notice a difference if I make it a habit after every run. Despite what some people say, I think it helps keep you injury free and running strong.