In June 1990, a small academic press published an initial run of 2,500

There seems to be a lot of useless information here to throw you off guard.

Let's say x books were sold between 1990-1995.

It says in the text "Total sales for the period from 1995-2000 represented an increase of 52 percent over total sales for the preceding five years."

So, 1.52*x books were sold between 1995-2000.

It then also says "For the period of 2000-2005, sales were double the sales for the previous five-year period."

This means, between 2000-2005, 2*(1.52*x) books were sold. (or 3.04*x)

Now look at the answer choices. We need to find x and 3.04x.
If we let x = 1320, then 3.04x should be around 4013, but there's no answer choice around 4013.
Next, let x = 1530. Then 3.04x should be around 4651. Aha! There's a choice for 4640, but let's just make sure there's nothing closer.
If we let x = 2530 (or more) then 3.04x = 7691 (or more), so we can eliminate the rest of the choices.

Thus your answer is 1530 and 4640.

Hope that helped.