Name the property which justifies this given 5x-10 conclusion 5 (x-2)

The distributive property. You distribute a number to several other numbers and/or variables. And the numbers that are receiving the distribution are surrounded by parentheses.

5 (x - 2) = 5x - 10

You distribute the number by multiplying each number/variable in the parentheses by the distributor.

The number 5 is the distributor and the variable x and the number - 2 is the recipients of the distribution.