If I want to fall asleep within 5 minutes, what works for me is varied physical and mental exercise throughout the day, and an easygoing book or movie near bedtime.
If there's something stressful going on the next day, a tech-nerd podcast like ATP helps me forget about it and get to sleep. But I try not to let late night podcasts become a habit - sometimes they get too interesting and I stay up for over an hour to keep listening.
As a puppy we could walk for an hour, or even more than 5km, and at home he'd still be a rambunctious little pest because he might be physically tired but not mentally. But a 5-10 minute training session, where he has to think? Out like a light on the couch for hours. I imagine it hits dogs harder than us because they're less suited to problem solving and intense thought in general. Now he gets bored if he doesn't get his training but a couple of sessions a day are good for him and easier than a long walk (shorter walks suit him fine now).
So it comes down to counting sheep type of distraction.
Like others echoed, if you pick an open ended unsolved mystery that is literally on your shoulders during the day, you'll be unable to switch off.