The degree of the polynomial obtained when $8-6x+x^2-7x^3+x^5$ is subtracted from$x^4-6x^3+x^2-3x+1$ is:

The correct option is D. $4$

According to the question,

$x^4-6x^3+x^2-3x+1-(x^5-7x^3+x^2-6x+8)$

$=x^4-6x^3+x^2-3x+1-x^5+7x^3-x^2+6x-8$

$=-x^5+x^4+x^3+3x-7$

Degree of the polynomial(that contains only one variable) is the highest exponent(power) of its various terms. The terms of the polynomial obtained are $x^5,x^4,x^3,3x$ and $7$. Here, the term $x^5$ has the highest power for the variable $x$ and hence the degree of the given polynomial is $5$.