Prevent 5V output on Arduino Nano 5V pin
A simple diode is all you need. The USB power already goes through a diode, so another diode the same will create a "highest voltage wins" situation.

That is, if the voltage provided by the USB port is higher than the voltage you provide on the +5V pin (after the diode's forward voltage drop) then the USB port will power the nano. If the voltage on the +5V pin is higher (after the diode's voltage drop) than the USB then the voltage on the +5V pin will power the nano.

No power will flow out of the 5V pin to your LED strip because the diode is in the way.

Connect the 5V external power to the anode of the diode, and the 5V pin of the Arduino to the cathode of the diode. The cathode is generally the end of the diode with the stripe.  Make sure the diode can pass enough current to power the Arduino when the USB is un-powered. The 1N4001 is a popular choice and very easy to get hold of.

That choice of diode also has a higher forward voltage drop than the on-board USB diode (0.7V as opposed to about 0.4V), so the USB will generally be chosen by default when connected and powered up, which is as it should be for a bus-powered device.