Certainly! Here are the rewritten sentences:

1. You may not like what I have to say, but you don't have to yell at me.
- You may not like what I have to say, but you don't have to shout your head off at me.

2. My brother is very attached to his stamp collection, and keeps it locked up.
- My brother holds his stamp collection dear and keeps it locked up.

3. She will probably be chosen for the beauty contest.
- She stands a good chance of being chosen for the beauty contest.

4. His theory was the opposite to the beliefs of his time.
- His theory ran contrary to the beliefs of his time.

5. What has this experience taught you?
- What conclusions have you drawn from this experience?