As the question states:
First one card is drawn and then put back into the bowl; then a second card is drawn.
It seems that there are 2 draws.

but I am not very sure about the answer.

(card 5 AND card 3) OR (card 3 AND card 5)
(1/6 X 1/6) + (1/6 X 1/6) = 1/36 + 1/ 36 = 2/36 = 1/18

i am not sure what i am missing ...

We already KNOW that the sum is 8.

To get a sum of 8, we can have:
- 4/4
- 5/3
- 3/5
- 6/2
- 2/6

2 possibilities out of 5 have a '5'

--> I would go with (D)

The answer is D. Can you tell me why the 1st explanation is wrong?

This is why the 1st explanation is wrong. The math is accurate, but it is not solving for what the question is asking for.

First, the only two possible combinations in which both cards total 8 and one of the cards is a 5 are:

1st draw 3; second draw 5
and
1st draw 5; second draw 3

The 1st explanation is solving for the probability of pulling a 5&3 or 3&5 out of all 36 possible outcomes.

The question assumes we pull two cards that total 8. So, all its really asking is, if we pull two cards that total 8, what is the chance that one of the two cards is a 5. Therefore, find the number of instances in which two cards total 8 (there are five possible combos; 2&6, 3&5, 4&4, 5&3, 6&2) and then see how many of those have a 5 card in them (only two of them do).

So, if there are five totals ways to get a sum of 8, there are only 2 instances that have a 5 in them:

2/5

Hope that helps