Forget about that Youtube video.
I watched it for a few minutes, and already noticed several 'mistakes'.
Dump the TIP127s. Scarse, because nobody wants to use them anymore.
Mosfets rule in this century.
Yes, you could use a buck converter, set to 5volt, to power the LEDs.
You could switch the LEDs low-side (in the ground line) with a TIP120.
~0.75volt loss across the "transistor switch" at that current, but that's acceptable in this case.
Use a 1k base resistor (not 2k2 or 3k3) for full saturation of the transistor.
You MUST use a current limiting resistor in series with that LED.
Volt drop across the CL resistor will be "5volt (supply) - 3.3volt (LED) - 0.75volt (TIP120)" = 0.95volt.
CL resistor value = 0.95V / 0.66A = 1.44ohm. Nearest value > 1.5ohm.
Power in resistor = 0.95 * 0.66 = 0.6watt (will get hot). Nearest > 1watt.
600-700mA LED current = 2watt (not 3watt as in the link), but better stick to that value.
Wise to NOT buy those LEDs, but the ones already mounted on a star base, for easier cooling (they get hot).
Post a diagram, showing the TIP120/LED/resistors, so we can check.
Some will probably say that you should use constant current drivers.
But a resistive dropper is cheaper/easier than eight CC LED drivers, and should be ok for the short time you're driving the LEDs.
Leo..