Does the 5 and 7 diet work

No, but I can say that most diets with any sort of name don't work, at least not for the long term.

Using My Fitness Pal works, provided it's used correctly (as in not entering sedentary if you're not, not entering a goal to lose 2lbs a week if you've only got 20 to lose, and coming in well below goal every day instead of aiming to have net cals as close to goal as possible).

TDEE method works (my personal favorite, which I've had my best success with http://www.myfitnesspal.com/topics/show/974888-in-place-of-a-road-map-2k13).

Basically, a reasonable calorie deficit works - it comes down to calories in/calories out.

My understanding is that 5:2 IS a calorie deficit eating plan - the only difference being that the deficit is done on the 2 'fast days' rather than having a small deficit each day - can someone on the plan confirm this?

I haven't tried it, but I will say I've heard good things from people doing it for health rather than weight loss. They find it easy to maintain, and physically feel better.

What you would need to make sure of is not to get mixed up with MFP's recommendations while doing 5:2. What I mean by this, is don't fill in all your stats here and get your target of 1500 cals a day (or whatever) and eat that for 5 days, and only 500 for 2 days. That would balance out way too low for the week, the 1500 already allows for your deficit.

I believe you'd need to (again, if someone can confirm) eat at your BMR for the 5 days, and then drop to the 500ish recommended for fast days.