Choice C is correct. The left-hand side of the given equation can be factored as $(5x + 3)(x - 8)$ . Therefore, the given equation, $5x^2 - 37x - 24 = 0$, can be written as $(5x + 3)(x - 8) = 0$. Applying the zero product property to this equation yields $5x + 3 = 0$ and $x - 8 = 0$. Subtracting $3$ from both sides of the equation $5x + 3 = 0$ yields $5x = -3$. Dividing both sides of this equation by $5$ yields $x = -\dfrac{3}{5}$. Adding $8$ to both sides of the equation $x - 8 = 0$ yields $x = 8$. Therefore, the two solutions to the given equation, $5x^2 - 37x - 24 = 0$, are $-\dfrac{3}{5}$ and $8$. It follows that $8$ is the positive solution to the given equation.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.