Is this a parallel circuit or series circuit? The picture shown is a lighting system with 5 leds and 5 resistors
It depens on the component you are looking at. One LED and one resistor are in serial. All LED and resistor pairs are in parallel to each other.
For distinction between parallel and series circuit its always a good measure to track where the current flows and look how many loops you can draw from Vcc to ground.
In this case you can draw 5 loops(indicates parallel) from Vcc to ground, one for each LED-resistor pair. In these loops the current has no other way than to flow through a resistor and after that through the LED(indicates series).