This is not my experience. The apps have not changed with time but they do become more unreliable and slower after prolonged usage. When I first upgraded to ios5, everything ran fairly smoothly for several months.
Same experience here. When I upgraded to 5, the only problem was Safari constantly crashing. That finally became less of a problem, but over the past couple of months, everything has gotten really laggy. For example, I'll tap a text box, and it will take a second or two for the keyboard to pop up, with similar delays for each character to appear after it's been typed.
I agree with filmbuff that "2 years old is not nearly old enough for a device to slow down like this." I have zero interest in buying a new iPad.