I've followed the steps for Recovery Mode on a iPhone 5 and get the connect to iTunes screen, but iTunes doesn't recognize the phone. Any ideas?

Greetings gska73,

Welcome to the Apple Support Communities!

I understand that you are trying to place your iPhone 5 in recovery mode, but iTunes does not recognize your iPhone. If this is the case, depending on the type of computer you are using, please use the appropriate link at the bottom of the attached article for further troubleshooting.

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

Get more help

Learn what to do if you don't see your device in iTunes for OS X, or in iTunes for Windows.

Cheers,

Joe