Convert everything to a rate of ploughing in ha per hour, then invert it. Working width \(W = 2 \times 0.5\ \text{m} = 1\ \text{m} = 0.001\ \text{km}\). At 5 km/h, the theoretical rate is \(A = W \times v = 0.001 \times 5 = 0.005\ \text{km}^2/\text{h} = 0.5\ \text{ha/h}\) (since 1 km\(^2\) = 100 ha).
Only 92% of the time is actually spent ploughing since 8% goes into turning, so the real rate is \(0.5 \times 0.92 = 0.46\ \text{ha/h}\).
Time needed for 23 ha is simply the area divided by this rate.
\[t = \frac{23}{0.46} = 50\ \text{h}\]\[\boxed{50\ \text{hours}}\]