We need some clarification. Did you subscribe to the creative cloud and the photography package (Photoshop & Lightroom $9.99/month)? If you did that, then it's probable that you have the standalone trial version installed. It will have to be uninstalled and you will need to install Lightroom from the creative cloud application manager.
This is the problem I am having. How can I uninstall my trail in order to install the lightroom 5 that i just purchased with the package?
You uninstall it the same way as you would uninstall any other application, there's nothing special that needs to be done other than you need first to logout of the Creative Cloud from the CC Desktop Application.
On Windows use the Control Panel>Programs & Features, select "Adobe Lightroom 5" in the list and click on the Uninstall button which appears at the top of the list when you have selected the program.
On OSX, drag the Adobe Photoshop 5.app from the Applications folder to the Trash.
Once uninstalled, restart your system, open the CC Desktop App, Login to your Adobe account, then on the Apps tab you should see Lightroom 5 with the "Install" button. Click on it and the install process will commence. Once complete, you're good to go.