Introduction:
To find the number of numbers greater than 23500 that can be formed using the digits 1, 2, 3, 4, and 5 without repetition, we need to consider the possible arrangements of these digits.

Analysis:
Let's break down the problem into smaller parts to simplify the analysis.

1. Thousands place:
Since the numbers need to be greater than 23500, the thousands place can only be filled with the digits 3, 4, or 5. This means we have 3 options for the thousands place.

2. Hundreds place:
Once the thousands place is filled, we can choose any of the remaining 4 digits (1, 2, 4, or 5) for the hundreds place. This gives us 4 options for the hundreds place.

3. Tens place:
After filling the thousands and hundreds places, we have 3 digits left (1, 2, and 5) for the tens place. This gives us 3 options for the tens place.

4. Units place:
Finally, for the units place, we have 2 remaining digits (1 and 4). This gives us 2 options for the units place.

Calculating the total number of numbers:
To find the total number of numbers, we multiply the number of options for each place value: 3 options for the thousands place × 4 options for the hundreds place × 3 options for the tens place × 2 options for the units place = 72.

Therefore, there are 72 numbers greater than 23500 that can be formed using the digits 1, 2, 3, 4, and 5 without repetition.

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