Final answer:
The difference of two polynomials of degree 5 is not always a polynomial of degree 5.
The degree of the difference depends on the specific polynomials involved in the subtraction.
Step-by-step explanation:
The degree of the difference of two polynomials is determined by the highest degree of the terms in the resulting polynomial.
If the highest degree term in one polynomial cancels out with the highest degree term in the other polynomial, the resulting polynomial could have a lower degree.
For example, if we subtract two degree-5 polynomials where the highest degree terms cancel each other out, the resulting polynomial could have a degree as low as 4.
Therefore, the degree of the difference of two polynomials depends on the specific polynomials involved in the subtraction.