Using Newton's second law, the equation of motion for the box is:

\(P - 8g \sin 5^{\circ} - F = 8a\)

For \(P = 7X\) and acceleration \(a = 0.15 \text{ m/s}^2\):

\(7X - 8g \sin 5^{\circ} - F = 8 \times 0.15\)

For \(P = 8X\) and acceleration \(a = 1.15 \text{ m/s}^2\):

\(8X - 8g \sin 5^{\circ} - F = 8 \times 1.15\)

Solving these equations simultaneously gives:

\(X = 8\)

Substitute \(X = 8\) into one of the equations to find \(F\):

\(F = 56 - 8g \sin 5^{\circ} - 8 \times 0.15\)

\(F = 47.8 \text{ N}\)

The normal reaction \(R\) is given by:

\(R = 8g \cos 5^{\circ}\)

\(R = 79.695 \text{ N}\)

The coefficient of friction \(\mu\) is:

\(\mu = \frac{F}{R} = \frac{47.8}{79.7}\)

\(\mu = 0.600\)