It looks like you have a recurrence relation or sequence defined by the formula \( a_n = n^5 n^2 - 3 \). However, there seems to be a formatting issue, as it could be interpreted in a couple of ways.

If you meant:
1. \( a_n = n^5 \cdot n^2 - 3 \), this simplifies to \( a_n = n^7 - 3 \).
2. If it's part of a recurrence, more context would be needed.

Could you clarify your question or provide more details about what you want to do with this expression? 

### Here are some related questions:
1. What specific properties of the sequence are you interested in?
2. Are you looking to find the first few terms of the sequence?
3. Would you like to analyze the behavior of the sequence as \( n \) increases?
4. Are you interested in finding limits or convergence?
5. Do you need help with any particular application of this sequence?

**Tip:** Always clarify whether you are working with a formula, a sequence, or a recurrence relation for more accurate assistance!

Explore the sequence defined by the formula a_n = n^7 - 3. This problem involves algebraic manipulation of powers and exponential growth in sequences. The step-by-step breakdown is ideal for students in Grades 10-12.

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