MYTS 2017 - Grade 9 - Round 2 Question 2

Let $f(x)=x^5-x^4-5x^3-x^2-x-1$ and $g(x)=x^3-x^2-5x-1$. The equation g(x)=0 has three distinct roots a,b,c. Find f(a)+f(b)+f(c).