The statement $(x + 5) - (x + 5) = 0$ illustrates the following rules of algebra:

1. Subtraction Property of Equality: This property states that subtracting the same quantity from both sides of an equation keeps the equation balanced. Here, $(x + 5)$ is subtracted from itself, resulting in $0$.

2. Additive Inverse Property: This property states that the sum of a number and its opposite (additive inverse) is zero. In this case, $(x + 5)$ and $-(x + 5)$ are additive inverses, so their sum is $0$.

Would you like more details or have any questions? Here are five related questions you might consider:

1. What is the difference between the additive inverse property and the additive identity property?
2. How does the subtraction property of equality relate to solving equations?
3. Can you explain the significance of the additive identity in algebra?
4. What other algebraic properties can be used to simplify similar expressions?
5. How can the distributive property be applied to more complex algebraic expressions?

Tip: Understanding the fundamental properties of algebra, like the additive inverse, helps simplify complex problems and solve equations efficiently.