I never got through to phone support, but I did get support via Chat. The first support tech had to elevate it to a superior. The level 2 support tech told me to: 1) uninstall version 5.5, and 2) download and install 5.6.
The 5.6 serial number and activation experience is completely different from 5.5, and this time it took my serial number OK.
Here's the link for 5.6 if you'd like to try this...it worked for me.
Adobe - Lightroom : For Windows : Adobe Photoshop Lightroom 5.6 : Thank You