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

\(\int (5 - 2x^2) \, dx = \int 5 \, dx - \int 2x^2 \, dx\)

\(= 5x - \frac{2x^3}{3} + c\)

We know that \((3, 5)\) is a point on the curve, so \(f(3) = 5\).

Substitute \(x = 3\) and \(f(x) = 5\) into the equation:

\(5 = 5(3) - \frac{2(3)^3}{3} + c\)

\(5 = 15 - \frac{54}{3} + c\)

\(5 = 15 - 18 + c\)

\(5 = -3 + c\)

\(c = 8\)

Thus, \(f(x) = 5x - \frac{2x^3}{3} + 8\).