Is the sum of two polynomials of degree 5 always a polynomial of degree 5? give an example to explain your answer

A counter example is

f(x)=5x^5+2x^3+3x
g(x)=-5x^5-x^4+x^2-4

Then f(x)+g(x) = -x^4+2x^3+x^2+3x-4  which is a polynomial of degree 4.

So the answer is no.  Counter-example is given above.

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.