Yes you need to consider them as separate, since two 5's can be obtained on any of the three dice, and would hence increase the probability.
The answer IMO is 1/24 as explained below (Kindly confirm if this is the
OA)
For getting a product divisible by 25, we need a 5 on atleast two of the three dice
So probability of getting a product divisible by 25 is 1/6 *1/6 *3 = 1/12
{We need to multiply by three since there are three ways of getting a 5 on atleast two of the three die namely, (1st 2nd) (1st 3rd ) (3rd 1st)}
Probability of getting an odd multiple is half of 1/12, which is 1/24 (since there is an equal probability of getting an even multiple and odd multiple, because there are an equal no. of odd and even numbers between 1 and 6)
So answer is 1/24.
Alternatively, Probability of getting 5 on two die and an odd number on the third die
= 1/6 *16* ½ *3 = 1/24 ( Multiplied by 3 for the same reason as mentioned above)