Choose the property that justifies the outcomes.
5(3*8)=15*8
associative property of addition
additive inverses
commutative property of addition
multiplicative inverses
distributive property
associative property of multiplication

It's obviously going to be a multiplication property, because multiplication is being used here.
It's not multiplicative inverses. (this is when two numbers, specifically something like 2 and 1/2, multiply to make 1)
It's also not the distributive property. An example of that would be if you had 5(3+8) and you multiplied the 5 into each term inside the parentheses to get 15+40.
The correct answer would be the associative property of multiplication, which states that you can multiply numbers together in any order. Here, we have 5 times (3 times 8), but the parentheses can be ignored because of this property. Then we would go ahead and just do the 5 times 3 to get the 15×8.