iPhone 5 and 5GHz WiFi

Probably a weak 5 GHz signal from the router. Have you tried a different 5 GHz router? My iPhone 5 works fine with three different 5 GHz routers (with SSID on). For testing purposes, try turning on SSID. (You can use a different SSID during the test if you are really concerned about broadcasting the real SSID.) If it still fails it means the router has a weak 5 GHz signal or you are too far from the router. 5 GHz does not propagate as well as 2.4 GHz, especially though walls.

the higher the bandwidth the easier a frequency is blocked by metal and wall and the likes

this is why GPS and sat disc's need a direct line of sight to the satellites and perform poorly in doors

as a security precaution, I do not broadcast my SSID for either band.

False sense of security. The SSID can be gleaned from other devices that are connected by a determined hacker. All you are doing is making it inconvenient. Better security is to require a strong password. It is no big deal that the SSID is seen by others. Without the password they can do nothing. I doubt your network is worth the effort from any determined hacker.