Controlling LEDs with bit bang method
You need to send the 5x24 bits out without a pause. If you then keep the line low for over 80us, that is interpreted by all LED drivers as the reset signal. It is not stated explicitly in the datasheet (at least I haven't found it), but I guess the reset signal means, that at that time all drivers will output the received values on the LEDs. That way you can light up all LEDs at the same time with their respective data.
The picture, that you refer to, explains the automatic data cascading. The first row is what you actually send from your microcontroller and also what is seen by the first LED driver in the row. That driver will then consume the first 24 bits, that it sees. After that, it will forward the rest of the data to the next LED driver. That will now consume the first 24 bits that it sees (thus the second 24 bits, that you have send). The third LED driver will do the same. But since in that example you only send data for 3 LEDs, no data is forwarded. Then the reset pulse happens and at some point in time you send a new set of data.
So each row represents, what the corresponding LED driver will see of the data, that you send. D1 sees all the data. Each following LED driver will see 24 bits less. D4 will see nothing, since you send only 3x24 bits in that example.