Sure! Here are the sentences re-written in the present perfect tense:
1. Asha has lived in Garowe.
2. They have kept all the students.
3. The boy has played the game.
4. She has written all the exercises.
5. The man has caught the rat.
In the present perfect tense, we use "has" or "have" followed by the past participle form of the verb. This tense is used to talk about actions that happened at an unspecified time in the past, actions that started in the past and continue into the present, or actions that have just been completed.