(a) Differentiate y with respect to x: \(\frac{dy}{dx} = \frac{1}{2}(5x-1)^{-1/2} \times 5\).

Use the chain rule to find \(\frac{dy}{dt} = \frac{dy}{dx} \times \frac{dx}{dt}\).

Given \(\frac{dx}{dt} = 2\), substitute to find \(\frac{dy}{dt} = 2 \times \frac{1}{2}(5 \times 1 - 1)^{-1/2} \times 5\).

Calculate \(\frac{dy}{dt} = 2 \times \frac{5}{2} = \frac{5}{2}\).

(b) Set \(2 \times \frac{1}{2}(5x-1)^{-1/2} \times 5 = \frac{5}{8}\).

Simplify to find \((5x-1)^{1/2} = 8\).

Square both sides: \(5x - 1 = 64\).

Solve for x: \(x = 13\).