Step 1: Find how much land the plough actually covers in one hour of running. In $1$ hour it moves $5$ km $= 5000$ m and cuts a $1$ m strip (2 bottoms of $0.5$ m each), giving a gross area of $5000 imes 1 = 5000$ m$^2 = 0.5$ ha.
Step 2: Since $8\%$ of every hour is lost in turning at headlands, only $92\%$ of the hour is spent ploughing, so usable output is $0.5 imes 0.92 = 0.46$ ha per hour of total time.
Step 3: To plough $23$ ha, divide the target area by this hourly rate: $\dfrac{23}{0.46} = 50$ hours.
\[oxed{50 ext{ hours}}\]