Do I need the 7805 Voltage regulator if I get power from the serial to USB?

I'm building a stand-alone device which will include an Arduino, but I wanna use the chip if the bare minimum necessary stuff. I'm reading this tutorial I wanna clarify though, that if I'm getting power from the serial to USB breakout (it's gonna be a controller for computer programs, so it will always be plugged in a computer), do I need the 7805 Voltage regulator or not? And if not, do I also need the two 10uF capacitors?, and if so, how do I wire them?

Hi, no you don't need the 7805. The 5V from the serial adaptor is already regulated. In fact, the 7805 wouldn't even work. It needs 6~6.5V to produce 5V.

Keep one of the capacitors. May not be neccessary, but a good idea in general. Simply wire it between 5V and 0V.