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. In this case, \( 5 \) was added to both sides of the equation.