Step 1 :Divide both the numerator and the denominator by \(x^2\): \(\frac{5 + \frac{3}{x} + \frac{1}{x^2}}{2 + \frac{4}{x} - \frac{7}{x^2}}\)
Step 2 :As \(x\) approaches infinity, the terms with \(x\) in the denominator approach 0: \(\boxed{\frac{5}{2}}\)