Sorry to burst your bubble, but 5lbs a week is not sustainable. The first week or two you diet, you might see that sort of loss. In the long run, however, you'll find yourself losing roughly 2lbs a week (which is still a decent amount).
The info that the site gave you about exercising doesn't seem too bad though. The pushups, situps, crunches, etc 3 days a week and the cardio workouts 3 times a week is a good model - training your muscles and working your heart throughout the week. There are still a ton of other workouts you can do with only your body which are much more effective, mind you.
Any form of exercise is beneficial, but the key to everything is your diet. What you put in your mouth will ultimately determine your level success.
Don't keep your heart set on 5lbs a week. If that were the average, a lot of people would be a lot skinnier, and this forum probably wouldn't have as many members

. You have to consider the fact that all this weight wasn't put on in a week or two - it took a while to gain all this weight, so it'll take a while to lose it as well. DON'T get discouraged if your weight loss slows down after the first couple of weeks. You have to understand that it's a process, however slow it may be.
Even when you get to the 2lb/week stage, you will probably have some weeks where, even though you're doing everything correctly, you don't lose even a pound. This is probably because your body has adapted to your schedule - the same workouts, the same foods, the same protein/carb/fat intake, etc. You always have to keep your body confused - never let it adapt! Switch up what and when you eat, or try changing your workouts.
This all might be a little preemptive as you've just started cutting, but keep it in mind.
As for your diet, I don't think you're eating enough. A common misconception among people who are new to weight loss is that the less you eat, the faster you lose. This is not true whatsoever. Your body
NEEDS a certain amount of calories per day to maintain your weight. In your case, it's probably around 2300 or 2400. To lose the pounds, you decrease this 'maintenance level' of calories by about 500. Overall you should be eating about 1800 or 1900 calories a day. By starving yourself (eating less than 1800), you're telling your body that food is scarce and you don't know when your next meal will be. You go into starvation mode and your body holds onto the extra energy it has stored in your fat cells for (literally) dear life.
You don't need to run away from fat like its the devil. There are 'good' fats and 'bad' fats. You should be getting your fats from sources like salmon and almonds, which are good fats.
Fruits are good to have in your diet, but they can be just as bad as candy in excess. Fruit is very high in sugar and consequently carbs. An apple, for example, has something like 100 calories and 20g of sugar.
You should be eating larger breakfasts as well. Try 1 whole egg and 2 or 3 egg whites - you get all the protein (which keeps you full) and none of the fat of the yolk.
Try to eat every 3 hours, or 5-6 times a day. This tells your body theres a constant source of food and it will let go of those fat stores quicker.
This is just a vague overview of a proper diet. At the top of this forum there are a bunch of stickies that have all the info you could ever need. Read through those then ask any questions you want.
Good luck