How Do I Measure the Time Duration of a Finite Length Discrete Sequence?
The following graphic should clear up why a useful answer is 5 seconds, consistent with conversions between the discrete-time and continuous-time domains. A good example of this are discrete time approximations to continuous time integration or differentiation where the inclusion of $\Delta T$ (sample period) is made. With all such approximations, the time duration attributed to each sample is one sample interval. For the Forward Euler approximation specifically, each sample covers the time duration up to and not including the next sample. Such as in the first graphic the time duration for a sample at $t=0$ is one sample interval of one second; up to and not including the next sample at $t=1$ when sampled at one sample per second, with a total time duration for the one sample as one second.
The bottom figure then shows how this would apply to five samples starting at $t=0$ resulting in a total time duration of 5 seconds.

The plot below shows the Forward Euler discrete-time approximation for the integration of a continuous time waveform $x(t)$, which would be given as follows in the formula below and demonstrated in the graphic, best showing how each sample carries the time duration of the sample period (and as David has pointed out in the comments, this equally represents the zero-order hold approach in the output of a typical Digital to Analog converter):
$$\int_0^{NT}x(t)dt \approx \sum_{n=0}^{N-1}x[n]T$$

The actual range of time used for each sample is specific to the analog-digital translation approach used, but would cover one sample duration in all cases, leading to a total duration of 5 seconds for the OP's case.