Made me chuckle. Your "just let them talk for 5 minutes", is another person's "wait until they're receptive to feedback." :)
I've never met a frustrated or angry person who is receptive to actual feedback. I'm the same way. Validate my emotional concern first, then move on to the next step.
Most of the time all I need to do is vocalize my problem... and that works best when I "have the floor."
If you don't mind me suggesting, that is really what was happening.