Let the areas above the time axis in the given $v$-$t$ graph represent positive displacement, and areas below the axis represent negative displacement.

In a velocity-time graph:

• Displacement $=$ signed area under the graph
• Distance $=$ total area under the graph, taking all areas as positive

From the graph over the total time interval of $25\,\text{s}$, the positive and negative triangular/rectangular areas add up such that: $\text{positive area} = 20$ $\text{negative area (magnitude)} = 5$

Therefore, $\text{Displacement} = 20 - 5 = 15$ $\text{Distance} = 20 + 5 = 25$

Hence the required ratio is $\frac{\text{distance}}{\text{displacement}} = \frac{25}{15} = \frac{5}{3}$

So the correct option is: $\boxed{\text{D }\left(\frac{5}{3}\right)}$