My car started this afternoon. I turned it off. About 5 minutes later I tried to start it again, but there was no sound. The lights come on, The battery is good. there is no sound (starter) at all

It is possible that there is no power to the starter motor.
So check from the following:
1. There must be power to the starter solenoid , use a multimeter to test.
2. If there is no power to the solenoid when the key is turned then the key switch is faulty.
3. Check if this is a diesel vehicle that the HEATER TIMER works and then allows power to the starter as the starter works only after the timer allows the heater to work.
4. if the solenoid works then the power at the starter must be checked, if not the solenoid is faulty.
5. finally if there is power to the starter motor but does not turn , it can be a jammed pinion, a faulty brush or a commutator. Replace starter motor if a cleaning wont help.