Start at the ledstrip at Pololu, and find the datasheet for the APA102C under the "Resources" tab.
The minimal voltage for a high level for the signals (VIH) is 0.7VDD.
With 5V, that minimal voltage is 3.5V (above 3.3V).
With 4.5V, that minimal voltage is 3.15V (below 3.3V).
There is a diode from VUSB to VIN, so when the power comes from the USB cable, then VIN (after the diode) is only 4.5V. If that is used to power the ledstrip then the minimal high level for the signals is below the 3.3V.
There is probably also a voltage drop in the USB cable, so the voltage to the ledstrip is lower than 4.5V, it might be 4.2 or so. That means the current to the ledstrip is a lot lower than with 5V. Perhaps there is also something wrong with the wiring that makes it less reliable.
If someone else has a weak 5V power supply and long wires, then there will be enough voltage drop to the ledstrip to make it work. You probably have a good strong 5V with good wires.
Do you understand that there is no 5V pin ? There is a hole in the board with some copper around it, but that is not connected to something (only the solder pad).