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The question in the image asks how many 5-digit numbers are smaller than 60,000. Let’s solve it systematically.

### Step-by-step solution:

1. **Understanding the Problem:**
   - A 5-digit number is between 10,000 and 99,999.
   - To ensure the number is smaller than 60,000, its first digit (the ten-thousands place) must be **less than 6**.
   - The digits can range from 0 to 9, but the first digit cannot be 0 (since it wouldn't be a 5-digit number).

2. **Splitting Cases by the First Digit:**
   - For numbers less than 60,000, the first digit can be 1, 2, 3, 4, or 5. This gives 5 choices for the first digit.

3. **Choices for Remaining Digits:**
   - Each of the remaining four digits can be any digit from 0 to 9 (10 choices each).

4. **Calculating Total Numbers:**
   - The total number of possibilities is:
     \[
     5 \times 10 \times 10 \times 10 \times 10 = 5 \times 10^4 = 50,000
     \]

### Final Answer:
There are **50,000 five-digit numbers less than 60,000**.

If the written solution you provided (32,805) seems different, it might involve additional restrictions not visible in the image. Please clarify if there are any special conditions for the digits.

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Would you like a detailed breakdown of the logic? Or have questions about a related topic? 

Here are some related problems for practice:
1. How many 4-digit numbers are smaller than 5,000?
2. How many 5-digit numbers are greater than or equal to 40,000?
3. If repetition of digits is not allowed, how many 5-digit numbers are smaller than 60,000?
4. How many odd 5-digit numbers are smaller than 50,000?
5. How many 5-digit numbers smaller than 60,000 have all distinct digits?

**Tip:** For problems involving restrictions, always isolate each restriction and calculate based on it step by step!

How many 5-digit numbers are possible that are smaller than 60,000?

Discover how to calculate the total number of 5-digit numbers smaller than 60,000 using combinatorics. Learn step-by-step how to account for digit restrictions to find the solution. Suitable for Grades 8-10.

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