Решение:
- At 8 o'clock last night, we were having dinner. (Past Continuous, т.к. действие происходило в определенный момент в прошлом)
- Be quiet! The baby is sleeping. (Present Continuous, т.к. действие происходит прямо сейчас)
- She has just finished her homework. (Present Perfect, т.к. действие произошло недавно и имеет результат)
- I will visit my cousin next weekend. (Future Simple, т.к. действие относится к будущему времени)
- They have not bought / haven't bought a new car yet. (Present Perfect, т.к. действие относится к периоду до настоящего момента, есть слово 'yet')
Ответ: 1. were having; 2. is sleeping; 3. has just finished; 4. will visit; 5. have not bought / haven't bought.