Interesting and debateable question,
Should I run before a 5k race?
I would say a qualified “No.”
Let me explain.
OK, first you DO need to warm up. But I would not warm up too much and stretch too much.
On the occasions where I have jogged very slowly to a 5k start I have not performed well. Preparation was otherwise perfect as were conditions. I have a sneaking feeling that I was reminding my muscles to run at a slow jog rather than race pace. So I cycle instead and they don’t have the opportunity to revert to a cycling action when I’m running!
I would imagine the best thing to do is:
1. Light stretch, focusing on any specific muscle groups that you have problems with
2. A few 100m ‘sprints’ at race pace.