**Ratio and Inverse Ratio:**

A ratio represents the quantitative relationship between two or more quantities. It is expressed in the form of a fraction or with a colon (:). For example, the ratio 5:7 represents a comparison between two quantities where the first quantity is 5 units and the second quantity is 7 units.

The inverse ratio is obtained by interchanging the positions of the quantities in the ratio. So, if the original ratio is 5:7, the inverse ratio would be 7:5.

**Given Information:**

According to the given information, the consequent of the inverse ratio is 5. In other words, the second quantity in the inverse ratio is 5 units.

**Finding the Antecedent:**

To find the antecedent of the inverse ratio, we need to determine the first quantity in the inverse ratio.

Let's assume the antecedent of the inverse ratio is x. So, the inverse ratio can be written as x:5.

Now, we know that the inverse ratio is 7:5. Comparing this with our assumption x:5, we can set up the following proportion:

7/5 = x/5

**Solving the Proportion:**

To solve the proportion, we can cross-multiply:

7 * 5 = x * 5

35 = 5x

Dividing both sides by 5:

35/5 = x

7 = x

Therefore, the antecedent of the inverse ratio is 7.

**Explanation:**

The given ratio is 5:7, and the consequent of the inverse ratio is 5. By setting up a proportion and solving for the unknown quantity, we determined that the antecedent of the inverse ratio is 7.

This means that if the original ratio is 5:7, the inverse ratio would be 7:5.