1. **Stating the problem:** We need to find the number of different 5-digit combinations possible on a lock with 5 wheels labeled 0 to 9 when successive digits must be different. 2. **Understanding the problem:** Each wheel can show digits from 0 to 9, so there are 10 possible digits per wheel. 3. **Case: Successive digits must be different.** - For the first wheel, there are 10 choices. - For each subsequent wheel, there are 9 choices because the digit cannot be the same as the previous one. 4. **Formula used:** The number of combinations with no two successive digits the same is: $$10 \times 9 \times 9 \times 9 \times 9 = 10 \times 9^4$$ 5. **Calculating:** $$9^4 = 9 \times 9 \times 9 \times 9 = 6561$$ $$10 \times 6561 = 65610$$ 6. **Answer:** The number of different 5-digit combinations possible if successive digits must be different is **65610**.