The PNAS study took the results of other research, but there isn't very much research into the effects of long-term regular fasting on disease in humans. Instead, most of the trials are in animals, or they looked at short-term changes - such as how well your cells repair themselves - which are linked to those diseases.
But, given those caveats, there is reason to be hopeful that "intermittent fasting" regimes such as 5:2 are good for you. First and foremost, it's about reducing calorie intake, and anything that does that, by and large, is a good move.
"In general, if you cut calories, you lose weight," says Prof Sattar. "A recent study in the Journal of the American Medical Association found that, no matter what the diet, you'll lose weight."
So, whether it's 5:2, paleo, Atkins or whatever, it's about eating fewer calories, not necessarily the specifics of the diet. And it is a straightforward step from there to reducing the dangers of Alzheimer's and cancer.
The link between obesity and cancer is well documented, and the blood-vessel damage caused by obesity and diabetes affect the veins in your brain as well as your body, which puts you at risk of dementia.
What's more, fasting itself may have benefits.
"A couple of small trials have found that people who diet strictly on 5:2 lose about the same weight as they would on a normal diet," says Susan Jebb, a professor of diet and population health at the University of Oxford, "but have slightly better metabolic results, which maybe is because the body isn't working as hard or producing as much insulin."
But, she warns, a lot more research is required before that can be confirmed.
There have been remarkable trials on mice, which showed that severely restricted diets - less than half what they usually eat - can lead them to live as much as two thirds longer than those which eat a normal amount. A similar thing might work on humans, says Prof Sattar, but "it would be a starvation diet - it wouldn't be a fun way to live."
Instead, if you want to live a longer and healthier life without starving yourself, the advice remains much the same as it ever has: maintain a healthy weight, eat a varied diet, take plenty of exercise. The 5:2 diet can be useful for that, says Prof Sattar, but "we don't know whether people can actually stick to it for 10 years. If they can't, then once they've used it to lose weight, they'll need to reduce their average daily calorie intake. And that's about retraining your taste buds. Choose one or two goals: cut out sugary drinks, brown bread instead of white bread, stop snacking."
Intermittent fasting diets, such as 5:2, may have benefits unconnected to the simple reduction of calories. But it is, at the moment, probably too early to say. A reduction of calories, though, is unarguably a good thing for a lot of us. And if it makes you feel like you're living more like our caveman ancestors, then that's no bad thing either.