Ben : Vivian = 5 : 7, so the total is 5 + 7 = 12 units.<br><br>Total savings = $\( w \), so 12 units = \( w \).<br>1 unit = \( \frac{w}{12} \).<br><br>Ben's savings = 5 units = 5 &times; \( \frac{w}{12} = \frac{5w}{12} \).<br><br>Final Answer: D: $\( \frac{5w}{12} \)