That's due to high levels of mercury isn't it? I think, like the egg/cholesterol thing, that they're a bit divided on that opinion.
However, I may be wrong, just going from stuff I've seen in magazines over here. Although I do still agree 5 a day is a bit much. A lot of American guidlines waver around a max of 6 a week, UK varies from 2 to practically unlimited.
"People can eat as much tinned tuna as they like, except women who are pregnant or are planning to get pregnant in the next year. These women should eat no more than four medium-size cans of tuna a week (with a drained weight of about 140g per can), or two fresh tuna steaks (weighing about 140g when cooked, or 170g raw)." (Taken from Food Standards Agency)
On topic, about 20 apples a day could be up to 1600kcal, which, depending on your weight etc, it your intake for the day.
Plus, which has already been said, eating tons of apples means eating tons of sugar. Why not buy in lots of varied veg and fruit to snack on? Maybe some avocado? High in good fats, so if you have it not so often, you're getting more nutrients than just from apples. Some berries and nuts maybe? Nuts are a good source of protein too, just again watch your calorie intake there.