The given question asks us to identify the number that does not belong to the given group of numbers: 3, 4, 5, 9, and 7. Let's analyze each number and determine the reason for their inclusion in the group or the outlier.

1. The number 3: This is a prime number, and it is the smallest number among the given options. It does not have any special characteristics that differentiate it from the other numbers in the group.

2. The number 4: This is not a prime number as it can be divided evenly by 2. It is also the only even number among the options. However, it doesn't stand out significantly from the other numbers in terms of its properties.

3. The number 5: This is also a prime number, just like 3. It is the only odd prime number among the options. However, this does not necessarily make it an outlier.

4. The number 9: This is a perfect square as it can be expressed as 3^2. It is the only perfect square among the options. This characteristic sets it apart from the other numbers in the group.

5. The number 7: This is another prime number, similar to 3 and 5. It is the largest prime number among the options. However, being a prime number does not make it significantly different from the others.

Based on the analysis above, we can conclude that the number 4 (option B) is the outlier in the given group. It is the only even number among the options, whereas the others are odd. Additionally, it is not a perfect square or a prime number, unlike the other numbers. Therefore, option B does not belong to the group.