7・112 A set of five-volume encyclopedias is arranged in ascending order on a bookshelf, i.e., from left to right, from Volume 1 to Volume 5. Now, we want to rearrange them in descending order, i.e., from left to right, from Volume 5 to Volume 1, but each time only the positions of two adjacent volumes can be swapped. What is the minimum number of such swaps needed to achieve the goal?
[Solution] By sequentially swapping the 1st volume with the 2nd, 3rd, 4th, and 5th volumes, the 1st volume can be moved to the far right position. Then, by sequentially swapping the 2nd volume with the 3rd, 4th, and 5th volumes, the arrangement of the 5 volumes becomes $(3,4,5,2,1)$. Next, perform the following swaps: $\{3,4\}$, $\{3,5\}$, $\{4,5\}$, resulting in the arrangement $(5,4,3,2,1)$, which involves a total of 10 swaps.

On the other hand, to change the arrangement of the 5 volumes from $(1,2,3,4,5)$ to $(5,4,3,2,1)$, the left-right order of any two volumes $A$ and $B$ must be reversed, which can only be achieved by swapping them when they are adjacent. Therefore, any two volumes must be swapped at least once, totaling at least 10 swaps. In conclusion, it is necessary to perform at least 10 swaps to achieve the required arrangement.