Now suppose that the 5 (identical) prizes will be distributed among the 8 people. a winner can receive more than one prize. in how many ways could the 5 prizes be distributed?

The answer to this question would be 792If A is the number of prizes and B is the number of people, the formula that needed to solve this question would be C(A+B-1, B-1) 
If you put the number it will become C(5+8-1, 8-1)= C(12,7)
Then the possible way should be:
12!/ 7! 5!= 479001600/ 120*5040= 792 ways

Coolio that’s so awesome thanks