Step 1: Understanding the ratios.
We are given that the milk-to-water ratios in the first and second vessels are 2:3 and 3:5, respectively. However, without knowing the amount of liquid in each vessel or the total quantities, we cannot determine the exact ratio of mixing. The quantities in each vessel are crucial for determining the final ratio of milk and water in the mixture.
Step 2: Conclusion.
Since we do not have the quantities of liquid in the vessels, the correct answer is (E) Cannot be determined.