Identify the mathematical property illustrated in the statement 7c + (a + 5b) = 7c + (5b + a).

The statement 7c + (a + 5b) = 7c + (5b + a) illustrates the commutative property of addition. This property states that the order in which two numbers are added does not affect the sum. In this case, the terms within the parentheses are rearranged from (a + 5b) to (5b + a), demonstrating that their order can be switched without changing the overall sum.

It's important to note that while the associative property relates to the grouping of terms—showing how numbers can be grouped differently when added—this question specifically focuses on changing the order of addition rather than the grouping. The distributive property involves distributing a multiplication over addition, and the identity property relates to adding zero to a number. Hence, these other properties do not apply here. The correct interpretation highlights how adding numbers in different sequences still yields the same result, reinforcing the concept of commutativity in addition.