In America, the way we talk about paper is amazingly convoluted. The short answer to your question is that 500 sheets of bond paper with a size of 17" by 22" have a weight of 20 pounds. The manufacturer would cut a sheet that big into four letter-size sheets, so a 500-sheet ream of 20 pound bond paper weighs 5 pounds.
If you had said it was something other than bond paper, then the size of a standard sheet used to determine the weight might be different. See the second link below for details. For example, Bristol paper is heavier and stiffer (like the paper in a manila file folder). Its standard sheet size is 22.5" by 28.5".
In general, the more a sheet of a certain grade of paper weighs, the thicker it is. You can purchase 20 and 24 pound bond paper at an office supply store. 24 pound bond paper is thicker, heavier and more opaque than 20 pound bond.
The metric system has a much better way of measuring paper. A0 paper is a square meter of paper. One side is 84.1 centimeters long and the other is 118.9 centimeters (the longer side's length is the square root of 2 longer than the shorter side's length). A1 paper is half of an A0 sheet (preserving the square root of 2 rule). A2 is half of an A1 sheet, and so on. And paper weight is measured in grams per square meter, so it is very easy to figure out what is going on!
Here are three useful links: