Bluetooth isn't setup directly from the menu on the d5600 and other SnapBridge enabled cameras. Instead, you have to use the WiFi or NFC linkage from the SnapBridge app to get your phone or tablet to pair with your camera on Bluetooth.

You can view or download the pairing guides and manuals (pdf) for the d5600 at this location: Nikon D5600 Download Center

I've only gone through this process with an iOS device and a D500, but here are the basics and the guides at the aforementioned link have the same steps:

1. Make sure your camera is not in Airplane mode.
2. Setup WiFi on the camera first, and note that the camera is hosting the WiFi network. You won't actually be able to connect the camera to an existing AP. You can set a password for this ad-hoc WiFi network on the camera.
3. Connect to the WiFi network from your device, using the name of the network and password for it that is configured on the camera.
4. On your camera, locate the "Connect to Smart Device" option in settings and activate it.
5. Launch SnapBridge on your device. If the WiFi connection dropped (this happens often on iOS), it may prompt you to activate it again. Simply go back to your WiFi settings or use the prompt button in the iOS Snapbridge app and reconnect to the AP/network hosted by the Camera when directed to the phone/tablet settings. Return back to the Snapbridge app after the wifi network is on the camera's AP.
6. If everything has gone well, it should detect the camera and you'll be prompted to verify the bluetooth code on both devices, and from here the pairing goes the same as any other bluetooth device, except that it is within Snapbridge.

Note that if your camera battery is not at 85% or better charge, you may have trouble connecting to the WiFi AP/network hosted by the camera. This is mentioned in the docs but worth repeating because out-of-the-box or after even moderate camera use, the camera's battery will not be fully charged and you will have to wait for a full charge to setup Bluetooth/Snapbridge. I carry an extra battery with me in the field if I anticipate needing to use SnapBridge.

Last, I had one more quirk that I couldn't duplicate, but just in case: If you setup a WiFi access password on the camera containing a space or an underscore, you might not be able to connect to it from your phone or tablet. I wasn't able to duplicate this issue again after the 1.06 patch for the D500, but if you've done the same, it may be worth trying a new password for WiFi that only has alphanumeric characters.