To find the volume of a right rectangular prism (which is the shape of the gift box), we can use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
In this case, the base area is given as \( 15 \) square inches and the height is \( 5 \) inches.
Now we can plug in the values into the formula:
\[ \text{Volume} = 15 , \text{in}^2 \times 5 , \text{in} = 75 , \text{in}^3 \]
Therefore, the volume of the gift box is \( \boxed{75} , \text{in}^3 \).