Решение:
- Jack was arrested due to having an alibi. (Причина, по которой его арестовали, несмотря на алиби).
- Although it was raining, Amy went jogging. (Союзы 'although' и 'even though' вводят уступку).
- They live in the city centre, due to the high crime rate. (Причина, по которой они живут в центре).
- The shop was burgled despite having security cameras. (Несмотря на наличие камер).
- Due to improved police work, there is less crime on the streets. (Причина уменьшения преступности).
Ответ: due to; Although; due to; despite; Due to.