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The volume of a right rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the base is 15 inches squared, so the length and width must be the square root of 15.
Therefore, the length and width are both √15.
Using these values, the volume of the gift box would be V = √15 * √15 * 5 = 15 * 5 = 75 cubic inches.