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The property of equality that justifies the step from \(3z^2 - 5 = 10\) to \(3z^2 - 5 + 5 = 10 + 5\) is the **Addition Property of Equality**.
This property states that if you add the same number to both sides of an equation, the two sides remain equal. Thus, the correct response is:
**Addition Property of Equality**