Your training programme for that day involves back squats, front squats, benchpress and saxon press. Before you start training you warmup by running nowhere for 5 minutes on the treadmill.
I seriously do not see the connection between running on the treadmill and weightlifting. How does running help you 'warm up' for a hard session of benchpresses and squats? Isn't it better to warmup for squats by doing... wait for it... squats? Squat with an empty bar first before you get to your main course. Or if an empty bar is your main course (don't worry, we all have to start somewhere), then squat with a pair of dumbbells. Or do bodyweight squats. Doesn't that make more sense?
That way your body gets better accustomed to what it is about to . You can run on the treadmill all you want but I bet you that it won't make you ready for an intense weightlifting session. The only thing that validates warming up on the treadmill is if you're about to have a good running session. And even then, why would you want to run on the treadmill when you're about to run outdoors?