To solve this problem, we need to find the amount of the mixture that should be replaced by water in order to achieve the desired ratio of milk and water. Let's break down the solution into steps:

Step 1: Understanding the Given Ratio
The given ratio of milk and water in the mixture is 2:1. This means that for every 2 parts of milk, there is 1 part of water in the mixture.

Step 2: Determining the Current Ratio
Let's assume that the current mixture contains 2x units of milk and x units of water. Therefore, the total amount of mixture is 2x + x = 3x units.

Step 3: Determining the Desired Ratio
The desired ratio of milk and water is given as 5:3. This means that for every 5 parts of milk, there should be 3 parts of water in the mixture.

Step 4: Determining the Amount of Mixture to be Replaced
Let's assume that y units of the mixture need to be replaced by water. Therefore, the new amount of milk in the mixture will be (2x - y) units, and the new amount of water will be (x + y) units.

Step 5: Setting up the Equation
According to the desired ratio, (2x - y)/(x + y) = 5/3.

Step 6: Solving the Equation
Cross-multiplying the equation, we get (2x - y) * 3 = 5 * (x + y).

Simplifying further, we have 6x - 3y = 5x + 5y.

Combining like terms, we get x = 8y.

Step 7: Determining the Amount to be Replaced
We are required to find the amount of the mixture that should be replaced by water. Since the total amount of the mixture is 3x units, the amount to be replaced is y units.

Substituting the value of x from step 6, we find y = x/8.

Therefore, the amount of mixture to be replaced by water is x/8 units.

Step 8: Final Answer
In conclusion, to achieve the desired ratio of milk and water (5:3), we need to replace x/8 units of the mixture with water.