Purchased the S5 on April 11th. All sound notifications are on. Phone not ringing. People call and tell me that they've been calling, but I'm not receiving a ringtone. Sometimes the only way that I know that a person has called, is after I received a voicemail notification.
7/13/2015 It's been 2 full weeks since my phone started not receiving phone calls. If I am on 4G LTE my phone will no ring. The only way I can get it to ring is if I initiate a call, something changed recently in the last 2 weeks. I notice now that when I call out the phone gets stuck for up to 10 seconds trying to connect the call. Something I was not experiencing up to 2 weeks ago. Now the only way to receive calls is to set it to CDMA and disable the 4G LTE function of my Galaxy S5. Way to go SPRINT, a real class act.
I fixed the problem of my Samsung Galaxy S5 not ringing when I got incoming (receiving) phone calls. Here's how:
Settings -> [Applications section, last one] --> Call --> Call rejection --> Auto reject mode: Make sure "Off" or "Auto reject numbers" is checked. (Not "All incoming calls" -- that was the problem on my phone, somehow in my pocket it had set itself to Auto-reject all incoming calls.)
Mine is a Samsung HAL-9000 [aka Galaxy S5]. Clever if lazy little bugger.