only if you're REALLY over-eating
Imagine a guy who weighs 160 pounds and has 8% body fat. Total fat = 12.8 lbs. He's in pretty good shape. If he aims to drop 5 lbs of all fat in 1 week, then he'll be at 155 lbs, fat weight of 7.8, and his body fat % would drop to 5%.
The question that I'd ask, though, is what type of calorie deficit would he need to lose those 5 lbs in that week? He'd need a deficit of roughly 3500 calories per lb, or in other words, 5 x 3500 = 17,500.
What is his maintenance level? If he's very active (but not competing in the Tour de France), it's probably in the ballpark of 3000 to 4000 calories total. Even assuming it is the high end of that range, that means that his total weekly calorie needs are 4000 x 7 = 28,000.
Our hypothetical guy would have to cut his calories down to 10,500 for the week, which averages out to 1500 calories per day. And his body would have to be able to continue working at its current activity level to keep the deficit that high and also be tailored to maintain all his muscle too (to make sure that only fat is lost).
Is this doable in one week? Of course. Would I recommend it? Of course not. Would I even want to go anywhere near someone attempting this? Hell no. He'll be hungry, irritable, frustrated at watching his performance drop, and tired as anything.
You can play with the math to see how other people would be affected, but note that the key comes from that very large deficit you have to create. Someone who manages to consume far more than they need could swing the 5 lb of fat/week plan. Anyone else, no matter how much they weigh, probably can't.
And when you see obese people lose a lot of weight in one week, they are not necessarily dropping pure fat. There is a lot of water fluctuation going on.