Do you mean that you would like an LED to come on and stay on when you use a 5V signal to set an FF?
If that is the case, you can use two cross coupled transistors to form a latch. Use the Q output to drive another transistor that has the LED in its collector circuit. The LED will light when you momentarily apply 5V to the SET input. It will go out when you apply 5V to the RESET input.
Alternatively, you can use a TTL flip flop such as a 7474
I agree with Mozikluv. You only need an SCR with the LED and a series resistor as its load. Trigger its gate to turn it on, and use a N/C push button in series with the LED to turn it off.