5. (10 points) There are 10 cards on the table, numbered $1, 1, 2, 2, 3, 3, 4, 4, 5, 5$. Now, these 10 cards are shuffled and arranged in a row from left to right. Then, count the number of cards between the two 1s, the two 2s, the two 3s, the two 4s, and the two 5s. The maximum possible sum of these 5 numbers is . $\qquad$
【Analysis】Place 10 cards in a row and number them from left to right as $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$. The number of cards between two cards $=$ the difference in their numbers - 1. The problem can be transformed into selecting 5 numbers from these 10 to be the minuends and the other 5 to be the subtrahends. Finally, subtract 5 to get the answer.

Finally, provide a specific arrangement to prove the feasibility of the answer.
【Solution】Solution: Place 10 cards in a row and number them from left to right as $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$. The number of cards between two cards $=$ the difference in their numbers - 1. The problem can be transformed into selecting 5 numbers from these 10 to be the minuends and the other 5 to be the subtrahends. The maximum value is $(10+9+8+7+6)-(5+4+3+2+1)-5=20$. Provide the following arrangement: $3,2,4,5,1,3,2,4,5,1$. Here, there are 4 cards between the two 1s, 4 cards between the two 2s, $\cdots$, and 4 cards between the two 5s; the total sum of the 5 numbers $=4 \times 5=20$. The answer is achievable.

Therefore, the answer is: 20