To find \(f(x)\), we need to integrate \(f'(x) = 3x^2 - 7\).

Integrating, we get:

\(f(x) = \int (3x^2 - 7) \, dx = x^3 - 7x + c\)

We know \(f(3) = 5\), so substitute \(x = 3\) into the equation:

\(5 = 3^3 - 7 \times 3 + c\)

\(5 = 27 - 21 + c\)

\(5 = 6 + c\)

\(c = -1\)

Thus, \(f(x) = x^3 - 7x - 1\).