The equation $5 \# 4 = 21$ seems to use a custom or unconventional operation symbolized by #. This is not a standard arithmetic operation, so we need to infer the logic behind this specific operation. One common pattern in such puzzles is to look for a relationship between the numbers that involves multiplication, addition, or some other arithmetic transformation.

Let's consider a few possibilities:

1. Addition and Multiplication Combined: $5 \# 4 = 5 \times 4 + 1 = 20 + 1 = 21$

2. Special Pattern or Formula: Sometimes these puzzles follow specific patterns. Another potential pattern could involve reversing digits, subtracting, or other operations, but we must confirm by checking more examples.

If there are additional examples provided with this same operation, it would help confirm the exact rule being used.

Would you like to provide more examples of this operation, or do you have any specific requirements for the logic used here?

Here are 8 related questions to expand on this topic:

1. Do you have more examples of operations using the # symbol?
2. What is the result of $7 \# 3$ using the same logic?
3. Can this pattern be generalized for any two numbers $a$ and $b$?
4. What is the result of $6 \# 2$ following this pattern?
5. Is there an alternative operation that also fits the given result?
6. How can we verify the correctness of the pattern for different numbers?
7. What if we reverse the operation: What could be the operation to get back from 21 to 5 and 4?
8. How would this logic be applied in a more complex mathematical problem?

Tip: Always look for patterns and relationships between numbers to solve unconventional equations. Testing multiple examples can help in identifying the correct rule or logic.