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The expanded form of the given expression \((a^2 - 5a + 2)(a^2 - a + 5)\) is:

\[
a^4 - 6a^3 + 12a^2 - 27a + 10
\]

Let me know if you'd like more details, or if you have any other questions.

Here are five follow-up questions you may find interesting:

1. How do you factor the resulting quartic equation?
2. How does this expansion compare to multiplying simpler binomials?
3. Can this expression be solved for specific values of \(a\)?
4. What are the roots of the polynomial \(a^4 - 6a^3 + 12a^2 - 27a + 10\)?
5. How would the graph of the polynomial look?

**Tip:** When expanding polynomials, it's helpful to multiply terms step-by-step, first handling the highest-degree terms, then proceeding to the lower-degree terms.

Learn how to expand the polynomial (a^2 - 5a + 2)(a^2 - a + 5) step by step. This problem involves key algebraic concepts such as polynomial expansion and the distributive law, ideal for students in grades 10-12.

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