Use the given digits `2, 3, 8, 9, 0` without repetition and make the greatest and smallest 5-digit numbers.

Answer

To solve the problem of forming the greatest and smallest 5-digit numbers using the digits `2, 3, 8, 9, 0` without repetition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The given digits are 2, 3, 8, 9, and 0.

2. **Forming the Greatest Number**:
- To create the greatest number, we need to arrange the digits in descending order (from largest to smallest).
- The largest digit is 9, followed by 8, then 3, then 2, and finally 0.
- Therefore, the greatest 5-digit number we can form is **98320**.

3. **Forming the Smallest Number**:
- To create the smallest number, we need to arrange the digits in ascending order (from smallest to largest).
- However, we cannot start a 5-digit number with 0, as it would make it a 4-digit number.
- The smallest non-zero digit is 2. So we place 2 first, followed by the next smallest digits in order: 0, 3, 8, and 9.
- Therefore, the smallest 5-digit number we can form is **20389**.

### Final Answer:
- The greatest 5-digit number is **98320**.
- The smallest 5-digit number is **20389**.