Every once in a while, there'll be a thread here that debates whether the average person, most people, or almost everyone can run a sub 5 mile given sufficient training. A lot of people say yes, but my personal experience indicates otherwise.
I've tried every possible way short of doping in my quest to get that sub 5 mile - low mileage, high mileage, live high/train low, live low/train high, training barefoot/in flats/in heavier trainers, different diets, etc. I've gotten multiple pacers, had enough sleep, run meets in different weather conditions, tried indoor tracks, run at different times of the day/night, and so on. You name it, I've probably done it (and yes, this included running on pure hate/rage/jealousy - last year, one of my former teammates managed to convince a college girl to run an all-out mile against me. Her PR was a tad under 5, and she wore a shirt that said "You got chicked" on the back. Didn't work - I failed to beat either her or my old PR, though I was on pace for a 4:58 mile at the halfway mark)
I'm in my late 20s, single, and have had plenty of time to train. Over the past couple years, I've pretty much made breaking 5 my life's mission, and the fastest I've run is 5:15.6. Taking EPO, steroids, HGH, and every illicit PED on the planet might get me to 5:03 or 5:02. If there is a dosage high enough to get me under 5, it would probably kill me long before I get near a track.
I can't blame obesity or bad genes for my failure to break 5. It's just an extremely tough time to achieve and a very impressive accomplishment if you have done it. At 5'6" and 112 lbs, I'm skinnier than most distance runners, and I had the muscle and leg speed to run decent times for the shorter distances. And while I never had anywhere near the amount of talent necessary to be an elite, I did have enough talent to win a few high school dual meets. My 400 and 800 PRs are 55 and 2:11.
I'll be the first to admit that the best I can offer is anecdotal evidence and not a scientific study, but if I couldn't break 5, there's no way that most people could. Maybe a 5 minute mile would be possible if you round mile times to the nearest minute and count a 5:29.99 mile as a 5 minute mile. But even that's pushing it.