Do they give you the weight of the normal sack or the total weight of all sacks?

Call the expected weight of a coin x. You know that four stacks have 5 coins that each weigh x, so each stack weighs 5x. One stack has coins that weigh y, where y < x, so this stack weighs 4y. You can take one coin from the first stack, two from the second, ..., five from the last. The expected weight of this stack is 1(x) + 2(x) + 3(x) + 4(x) + 5(x) = 15x. Your scale will give you a smaller number, and the difference between 15x will tell you which stack has the light coins. For example, if x = 1lb and y = 0.9lbs, and your scale tells you 14.6, you know that you must account for 0.4lbs. If each light coin has a 0.1 deficit, you know there were four of those coins, so stack 4 has the light coins.

Should have specified that all the coins in the special stack weigh 1 pound less, not just some of them.