1. The problem asks to find the curved surface area of a cylinder with height $16$ cm and radius $5$ cm. 2. The curved surface area $A$ of a cylinder is given by the formula: $$A = 2 \pi r h$$ where $r$ is the radius and $h$ is the height. 3. Substitute the values $r = 5$ and $h = 16$ into the formula: $$A = 2 \pi \times 5 \times 16 = 160 \pi$$ 4. Calculate the numerical value of $160 \pi$: $$160 \pi \approx 160 \times 3.1416 = 502.6548$$ 5. Round to 1 decimal place: $$502.7$$ 6. Therefore, the curved surface area of the cylinder is $502.7$ cm${}^2$ to 1 d.p.