There are two possible causes why such problem occurs. Either it is due to the phone's silent mode is on or phone volume is extremely low.
1. Make sure silent mode is OFF.
You're right. This thing is definitely very basic but many would neglect this among the causing factors as to why such problem on the handset occurs. If silent mode is set to ON or enabled on the phone, you will not be able to hear the phone ring when receiving calls as there will be no incoming call alert to sound.
In this case, ensure Silent mode is turned OFF.
2. Check the volume and make sure it is not set to 0. Remember than if the ring volume on your phone has been set to 0, you will not be able to hear incoming call alert sound.
Here's how to adjust your phone's ring volume:
2.1. Tap on the upper or lower part of the Volume key and select the required ring vol ume.
If problem persists, then I suggest you try updating your phone's software (if you haven't done this recently). Majority if not all software updates are released to add new functionality and resolve existing issues on your device.
In case you haven't yet contacted Samsung Technical Support regarding this issue you have with your Galaxy S5 handset, I suggest you do it now to let them assist you further in troubleshooting the problem.