I know people don't want to hear this, but I lost 40 pounds in exactly 2 months as of today (April 5- June 5). That was not my goal, and I ate healthily (1600 calories a day as I'm breastfeeding). I never have had a supply with my milk, so I have not worried about not eating enough. I started out only running 15 minutes a day, but now I've increased to running 1/2 hr a day and speedwalking for 15. That's it. I lost weight before and I also lost about 15-20 pounds a month, although then I only ate 1200 calories a day as I didn't have to factor in extra calories for milk supply.
I'm assuming from your ID, that you are a male, and men tend to lose weight faster than females. My hubby has lost 20 pounds in a few months just by eating a LITTLE healthier. No working out, and still ate snacks at night. (*******, lol). And if you ever watch Biggest Loser, the guys there lose weight like crazy compared to the girls.
It also depends on your size (I didn't see any figures mentioned on your profile so not sure). If you are larger, the weight comes off faster. (I do not expect to keep up this rate of loss much longer).
So I think if you really exercised and ate carefully, there is no reason why you couldn't comfortably lose 40 pounds in 2-5 months.
As for the trying to eat healthy, I am not gonna lie...it sucks, lol. It does help that I am already a vegetarian. For me, eating healthy means cutting out alot of the crappy carbs I used to eat, and sugar. I still allow myself healthy fats like some butter, cheese, etc. I try to find things I like and are low cal (veggie fajitas, without tortillas and using greek yogurt/lemon juice as sour cream for example) and then I can eat a TON and it is still only about 500 calories. For a person who likes to fill her plate, the small portions of dieting really get to me, so I search for recipes I like where I can feel full
As for binging, I chew a LOT of gum, lol. I buy the healthy aspartame free stuff in bulk (amazon), and then chew pretty much all day. And if I have a really bad craving, I allow myself some healthy hard candy to suck on for a while, and that helps. Not sure what your favorite binge foods are, but if you can find healthier alternatives, that helps. I LOVE pizza (who doesn't) dipped in ranch. So I make my own now using tortillas, and "ranch" I make from ranch mix/greek yogurt. I can eat a few tortillas with as much of the ranch as I want (which honestly doesn't taste much different from the real stuff), and it is still way less calories than one piece of real pizza. Little things that give you comfort help in the long run...hope that makes sense! Good luck