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 you can add the same value to both sides of an equation without changing the equality. In this case, adding 5 to both sides of the equation allows you to isolate the term involving \( z \).