Suppose that $f$ is a polynomial such that \[(x^2-1)\cdot f(x)=5x^6-x^5+3x^4+x^3 - 25x^2 +38x -17.\]What is the degree of $f$?
Since the product of $f$ and a polynomial with degree 2 equals a polynomial with degree 6, we know that $f$ is a polynomial with degree $6-2=\boxed{4}$.