Regulated Power Supply
If you look at a typical 7805 datasheet  you'll find a statement like

Note: Minimum load current for regulation is 5 mA

If the circuit is expected to maintain a 5V output with a load going right down to zero, the resistor R ensures that enough current is drawn from the 7805 to guarantee that the 5mA minimum is met. In this case a 1000 Ohm resistor would be needed.

It's often not seen in the real world because the 7805 will normally be built into a circuit that will always take at least the minimum load.