The degree is simply the highest exponent of the variable.
Separately p(x) = 5x^5-3x+7 is degree 5. q(x) = 3x^2-9 is degree 2.
p(x)*q(x) is multiplication. All you need is the degree so all you have to do is add the two degrees 5 + 2 = 7.
You can multiply the terms with the highest exponents to get the same results since you don't need to simplify,
5x^5 * 3x^2 = 15x^7 which is degree 7.
You could carry out the multiplication to see that the other terms will have smaller exponents.
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