Be involved in v. engage v. participate v. prosecute v. pursue

I would like to ask you about the difference between the verbs "to be involved in" , "to participate" and "to pursue". For this phrase "to pursue an activity" and for these sentences.

1. "She was involved in many activities."

2. "She engaged in many activities."

3. "She participated in many activities."

4. "She prosecuted in many activities."

5. "She pursued many activities."

http://www.wordwebonline.com/en/PURSUE

Thank you.