To find the smallest 5-digit number using the digits 0, 2, 4, 6, and 8, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Digits**: The digits we have are 0, 2, 4, 6, and 8.
2. **Determine the First Digit**: The first digit of a 5-digit number cannot be 0, as it would then be a 4-digit number. Therefore, we need to choose the smallest non-zero digit. The smallest digit we have is 2. So, we place 2 as the first digit.
**First Digit**: 2
3. **Arrange the Remaining Digits**: After placing 2, we have the digits 0, 4, 6, and 8 left. To create the smallest number, we should place the smallest remaining digit next.
4. **Place the Next Digits**: The next smallest digit is 0. We can place 0 in the second position.
**Second Digit**: 0
5. **Continue with the Next Digits**: Now, we have the digits 4, 6, and 8 left. The next smallest digit is 4, so we place 4 in the third position.
**Third Digit**: 4
6. **Next, Place the Remaining Digits**: Now we have 6 and 8 left. The next smallest digit is 6, so we place 6 in the fourth position.
**Fourth Digit**: 6
7. **Finally, Place the Last Digit**: The only digit left is 8, which we place in the last position.
**Fifth Digit**: 8
8. **Combine the Digits**: Now, we combine all the digits we have placed to form the smallest 5-digit number.
**Final Number**: 20468
### Conclusion:
The smallest 5-digit number using the digits 0, 2, 4, 6, and 8 is **20468**.
