I have been experiencing 5.0 Ghz connectivity issues for months. Got my Samsung Galaxy S4 nearly 1 year ago. Got a NETGEAR Nighthawk R7000 router a couple of months later. For about 2 months, the 5.0 Ghz connection on the phone worked just fine. Then I started getting intermittent messages from the phone saying that the 5.0 Ghz connection was unstable. I switched to the 2.4 Ghz network, and everything worked flawlessly. Then in October 2014, a ton of issues erupted on the router. Best Buy was kind enough to exchange the router, but right out of the box, the new router demonstrated many of the same issues (issuing duplicate IP addresses to client devices, intermittent reboots, etc.). Long story short, working with NETGEAR tech support, all those issues have been resolved. I signed a non-disclosure agreement, and am now on my third or fourth beta version of their firmware (V1.0.4.20_1.1.54). The Galaxy S4 5.0 Ghz connection is the only outstanding difficulty I am having.
So, earlier today, I went to my local Best Buy to see if my phone would connect to their 5.0 Ghz WiFi network. Lo & behold, my phone demonstrated the same issues it did on my home network, leading me to conclude that the problem rests with the phone. Disabling my 5.0 Ghz network security does not solve the problem. Even though the phone is in the same room with the router, the phone shows the 5.0 Ghz network intermittently as "Not in range." I am now working with Samsung via their live chat tech support to see where that gets me.