Cheerful illustration of a bluebird in a tree, paired with a poem about nature and birds.

Problem Analysis:

The task involves solving a word problem related to Blue Sikes and his birdhouse. The problem is presented in the form of a story, and we need to extract the relevant information and perform calculations to find the solution.

#### Key Information from the Story:
1. Initial Condition: Blue Sikes had 5 birds in his birdhouse.
2. First Event: Three more birds flew into the birdhouse.
3. Second Event: Two birds flew out of the birdhouse.
4. Question: How many birds are left in the birdhouse?

Step-by-Step Solution:

1. Start with the Initial Number of Birds:
- Blue Sikes initially had 5 birds in his birdhouse.

2. Add the Birds That Flew In:
- Three more birds flew into the birdhouse.
- New total: \( 5 + 3 = 8 \) birds.

3. Subtract the Birds That Flew Out:
- Two birds flew out of the birdhouse.
- Final total: \( 8 - 2 = 6 \) birds.

Final Answer:

After performing the calculations, the number of birds left in the birdhouse is:

\[
\boxed{6}
\]

Explanation:

- We began with 5 birds.
- Adding 3 birds increased the total to 8.
- Subtracting 2 birds reduced the total to 6.
- Therefore, there are 6 birds remaining in the birdhouse.

This method ensures that we account for all changes in the number of birds step by step, leading to the correct final answer.