Replying to my own question here.
I contacted support via telephone and they helped me figure it out. Here is the issue:
If you create a network using the Hamachi client (and not from the website), using a FREE 5-user account, it does NOT automatically attach itself to your LogMeIn profile/account. Strange, I know. The client works fine and you can give your network ID to other users to connect to and use (up to 5 of course) but it will not show up in your online profile/account. The best solution is to create your network online while logged onto your account on the website and create the network there. This will then know the correct status of your account and the correct number of maximum users.
For those like me who had already created a network with the free, 5-user version, you will need to delete this network from the client (I can’t remember if I right-clicked on the network name, used the Manage menu or the Network menu). You can then recreate the network from the web page tool using ADD NETWORK. The good news is, you can use the same network ID you just deleted. When you do this, go back to the Hamachi client and you will see that new network now in the client. If you used the same network name, it will look like the same network that you deleted and you could get the mistaken impression that the Delete Network did not work. It did. You have just added it back in from the website.
One last note, when you create the network online, it will look like you are being offered the option to use the free, 5-user version, or buy the $49 version (or higher) that you thought you already bought. There is a drop-down where it says Free 5-user. Click the drop-down arrow and you will see the account level you have already purchased there.
