Have I missed something here?
I can't find any description of what "Arduino" as actually being used here. The use of a 74HCT14 or 74HCT04 is only relevant if using a 3.3 V logic microcontroller, otherwise a 74HC14 for 5 V logic.
The Arduino should be powered by the same 5 V power supply as the LED strips. The power to the Arduino should come back to it along with the data wire from the common distribution point - which is where you would mount the 74HC14. The series resistors should connect at the "DIN" of each strip, not at the distribution point.
If using a UNO, (only) the "5V" pin should be disconnected from your 5 V main power supply whenever you connect the USB to a PC for programming.