To determine the maximum number of turning points of a polynomial, we can use the following rule:

A polynomial function of degree $n$ can have at most $n - 1$ turning points.

The given function is: $y = 5x^6 - 3x^4 + 2x - 9$ This is a 6th-degree polynomial (the highest exponent of $x$ is 6).

Using the rule, the maximum number of turning points is: $6 - 1 = 5$

Thus, the correct answer is:

5.

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Would you like further explanation or details on turning points? Here are some related questions for practice:

1. How do you find the actual turning points of a polynomial?
2. What is the difference between a turning point and an inflection point?
3. How does the derivative of a function help in finding turning points?
4. Can a 6th-degree polynomial have fewer than 5 turning points?
5. How can you use the second derivative to classify turning points?

Tip: The turning points occur where the derivative of the function equals zero.