To solve this problem, we can use the concept of distributing identical objects into distinct boxes. We need to find the number of ways to distribute 8 different dolls into 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys.

Let's consider the number of dolls in each box as follows:

- If one box holds all the dolls, there are 5 ways to choose which box will hold all the dolls. Once we have chosen the box, we can arrange the dolls in that box in 8! ways (since the dolls are different). The remaining 4 boxes can be left empty in 1 way. Therefore, the total number of ways is 5 * 8! = 20,160.

- If two boxes hold all the dolls, there are 5C2 ways to choose which two boxes will hold all the dolls. Once we have chosen the boxes, we can arrange the dolls in those boxes in (8!)/(2!2!) ways. The remaining 3 boxes can be left empty in 1 way. Therefore, the total number of ways is 5C2 * (8!)/(2!2!) = 10 * 8!/(2!2!) = 10 * 8 * 7 * 6 = 2,240.

- If three boxes hold all the dolls, there are 5C3 ways to choose which three boxes will hold all the dolls. Once we have chosen the boxes, we can arrange the dolls in those boxes in (8!)/(3!3!2!) ways. The remaining 2 boxes can be left empty in 1 way. Therefore, the total number of ways is 5C3 * (8!)/(3!3!2!) = 10 * 8!/(3!3!2!) = 10 * 8 * 7 = 560.

- If four boxes hold all the dolls, there are 5C4 ways to choose which four boxes will hold all the dolls. Once we have chosen the boxes, we can arrange the dolls in those boxes in (8!)/(4!4!) ways. The remaining 1 box can be left empty in 1 way. Therefore, the total number of ways is 5C4 * (8!)/(4!4!) = 5 * 8!/(4!4!) = 5 * 70 = 350.

- If all five boxes hold all the dolls, there is only 1 way to distribute the dolls.

Now, we can add up all the ways from each case to get the total number of ways:

Total number of ways = 20,160 + 2,240 + 560 + 350 + 1 = 23,311

Thus, the correct answer is option (a) 23,311.