It seems like you're exploring an unconventional operation or notation with $5 \& 4 = 21$. In standard arithmetic, $5$ and $4$ do not equal $21$ under basic operations like addition, subtraction, multiplication, or division. Here are a few possibilities of what this could mean:

1. Custom Operation: You might be defining a custom operation $\&$ where $5 \& 4 = 21$ by a specific rule.
2. Concatenation: It could mean the concatenation of digits 5 and 4 to form 54, but this does not explain the resulting 21.
3. Base Conversion: It could be some form of base conversion, but standard base conversions from 5 and 4 don't result in 21 in any conventional base systems.
4. Typographical Error: It could also be a simple typographical error.

If you meant to indicate something specific, please clarify the operation or the context. Here’s how the standard operations on 5 and 4 work:

• $5 + 4 = 9$
• $5 - 4 = 1$
• $5 \times 4 = 20$
• $5 / 4 = 1.25$

Would you like to explore a specific type of custom operation, or do you have another mathematical problem in mind?

Here are some questions related to different mathematical operations:

1. What is the result of $7 + 3$?
2. How do you perform subtraction with negative numbers?
3. Can you explain the concept of division as repeated subtraction?
4. What is the product of $6 \times 8$?
5. How do you solve $5^2$?
6. What is the result of $12 \div 3$?
7. Can you demonstrate how to use the associative property in multiplication?
8. What are the steps to solve $3x + 4 = 19$ for $x$?

Tip: Always double-check your equations for any potential typographical errors, as they can lead to incorrect results.