To find the equation of the curve, we need to integrate the derivative \(\frac{dy}{dx} = 2x^2 - 5\).

Integrating, we get:

\(y = \int (2x^2 - 5) \, dx = \frac{2x^3}{3} - 5x + c\)

We use the point \((3, 8)\) to find the constant \(c\).

Substitute \(x = 3\) and \(y = 8\) into the equation:

\(8 = \frac{2(3)^3}{3} - 5(3) + c\)

\(8 = \frac{54}{3} - 15 + c\)

\(8 = 18 - 15 + c\)

\(8 = 3 + c\)

\(c = 5\)

Thus, the equation of the curve is:

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