Macbook failing to connect to 5GHz networks

Most likely your Airport Card has failed.

On your particular Mac, it uses the BCM94360CS custom SoC (System on Chip) that supports dual-band WiFi and Bluetooth. The critical part related to your issue is the "dual-band" WiFi; it uses two different radios, not one. So, it's completely plausible that one radio has failed (5GHz) while the other (2.4GHz) continues to function; this is what you're seeing.

^{Image from iFixit.com}

To verify that it's not a software issue, you should boot into Safe Mode (hold ⇧ Shift) and/or Recovery Mode (⌘ Command R). If the problem persists, it's a hardware issue.

You'll just need a replacement AirPort adapter which is fairly inexpensive. It's also a fairly straight forward fix, basically remove the back cover, disconnect the Wi-Fi and Bluetooth antenna, then remove the AirPort card. Replace with the new one and reverse the procedure to reassemble everything. iFixit.com has an excellent step-by-step guide you can follow.

However, if opening the back of your Mac is not your cup of tea, let a professional handle it for you.

My iMac late 2012 wasn't connecting to the new 5Ghz 802.11/ac router, so I followed along Allan's answer and bought a new Airport Card. The problem remained.

The real issue was that when i setup my router as Access Point it doesn't show options for wifi mode(802.11a/b/g/n/ac). My iMac can only do 802.11a/b/g/n, and I can't connect to the 5Ghz because the router it's only doing 802.11ac instead of what I was expecting to be 802.11n/ac mixed.

So, before buying a new airport card, try changing the router mode and broadcasting channel to your Mac's supported. (About this Mac->System Report->Network->Wifi->Supported PHY Modes & Supported Channels)

My solution was buying a 802.11ac wifi usb adapter and enjoy the faster speeds.

Sorry to answer again the same question but the channel was the issue on my 2012 (and several other) macbooks as well. go 48 or lower for the 5Ghz network. Cameron is correct.