No you can't eat 5000 calories a day and not gain. I've overeaten while consuming only 20 grams of carbs/day myself. I gained. I can provide more details if you really need to know.

As I remember, Atkins, Eades, Pescatore, Schwarzbein ... all of them say not to overeat. Pescatore especially emphasizes not overeating. Not overeating is not the same thing as severely restricting yourself. You can generous, lavish amounts of food and still lose. On this site, people use a rule of 10 - 12 times your bodyweight in pounds to yield the number of calories you should consume in a day for optimal weight loss. That's a lot.

But you can't go on wild, reckless binges without consequence and none of the books say you can.

~Mel