To find \(f(x)\), we need to integrate \(f'(x) = 3x^2 + 2x - 5\).

The integral of \(3x^2\) is \(x^3\), the integral of \(2x\) is \(x^2\), and the integral of \(-5\) is \(-5x\). Therefore,

\(f(x) = x^3 + x^2 - 5x + c\), where \(c\) is the constant of integration.

We use the point \((1, 3)\) to find \(c\). Substituting \(x = 1\) and \(f(x) = 3\) into the equation:

\(3 = 1^3 + 1^2 - 5(1) + c\)

\(3 = 1 + 1 - 5 + c\)

\(3 = -3 + c\)

\(c = 6\)

Thus, \(f(x) = x^3 + x^2 - 5x + 6\).