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.

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!