Question

is f(x)=x+x+5 a linear function?

Answer 1

can it be written in the form f(x) = ax+b?

Answer 2

actually ax+b is not linear
linear implies it goes through the origin (common mistake that most everyone makes).
so mx+b is called affine when b is not 0

Answer 3

but im guessing your teacher also makes this mistake and thus considers the function given as linear. so yes:)
But tell him/her its not linear its affine and see what they say:)