There are really two things wrong with the block diagram and the description.
Firstly, where are the anti aliasing and reconstruction filters, these are kind of important to reconstructing a signal that actually resembles the input. In particular that output graph is taken before the reconstruction filter which is a vital part of making a DAC actually output analogue....
The requirement is that the sample rate MUST be greater then twice the bandwidth present at the sampler input, and the output must be filtered to a bandwidth less then half the sample rate.
Secondly, you really need dither (canonically triangular probability distribution noise added at the input with a peak level equal to 1 quantisation step), this makes the quantiser output switch between two states such that the average value exactly matches the input. It converts a non linear system with discrete steps to a linear one with noise, do this right and you can hear signals below the broadband noise floor.
If that lot came from a text book of some kind, it is a horrible description probably written by someone who has never actually implemented a digital voice channel (Apart from anything else, 5ks/s is really too slow, even the phone system uses 8k, for an audio bandwidth of approximately 3.5kHz).