To find the limit of the function (x^2 - 1) / (5x^2 + 4x - 1) as x approaches infinity, we need to look at the leading terms of the numerator and denominator.

As x approaches infinity, the terms x^2 and 5x^2 in the numerator and denominator dominate the expression. So, the limit can be approximated by dividing the leading terms to get:

(x^2 / 5x^2) = 1/5

Therefore, the limit of the function as x approaches infinity is 1/5.