Given:
There are given that the total number of hats is 25.
Step-by-step explanation:
First, we need to find the number which is a multiple of 5 and 5:
So,
The number which is multiple of 5 is:

And,
The number which is multiple of 6 is:

Now,
We can see that the total number which is a multiple of 5 is 5.
So,
The probability is:

And,
We can also see that the total number which is a multiple of 6 is 4:
So,
The probability is:

Now,
The probability that the slip of paper show a number that is multiple of 5 or 6 is:

Final answer:
Hence, the probability is 0.032.