Q: Can't use Keynote Remote Because of iPhone 5's Bluetooth

Here's Apple's instructions:

Using Keynote Remote with Bluetooth

When a Wi-Fi connection is unavailable you can use Keynote Remote with Bluetooth to control your Keynote slideshow from one iOS device to another (iPad, iPhone, iPod touch). However, slides may take longer to appear on Keynote Remote when connected via Bluetooth. You cannot use Keynote Remote via Bluetooth with a Mac. The following steps use Keynote Remote on an iPhone to control a Keynote presentation on an iPad via Bluetooth.

1. iPhone: Go to Settings > General > Bluetooth and turn Bluetooth ON.
2. iPad: Go to Settings > General > Bluetooth and turn Bluetooth ON.
3. iPad: Open a Keynote presentation.
4. iPhone: Open the Keynote Remote app. If you have previously paired your iPhone or iPad, you can immediately begin to control your slideshow from your iPhone by tapping Play Slideshow. If this is the first time pairing with these iOS devices, refer to the steps in "Linking Keynote Remote to Another iOS Device," above.
   
   Note: If your iPhone displays the message "No connection available. Both devices must be connected to a Wi-Fi network or have Bluetooth turned on," continue with the steps above because you may still be able to use Keynote Remote with Bluetooth

The complete Apple instructions are here: http://support.apple.com/kb/HT3325

The key sentence in the instructions which answers your question (unfortunately in the negative) is this:

"You cannot use Keynote Remote via Bluetooth with a Mac".

Sorry.