\(f\left(x\right)=x^5-2009x^4+2009x^3-2009x^2+2009x-2010\)
\(f\left(2008\right)=x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-2010\)
\(f\left(2008\right)=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-2010\)
\(f\left(2008\right)=x-2010=2008-2010=-2\)