Perhaps you didn't give all the details. When purchasing an upgrade version of Lightroom, you need the serial number of the original version of Lightroom that you purchased as well as the serial number from the upgrade version. Upgrades like from version 4 to 5 need to be purchased. A serial number from Lightroom 4 will not activate Lightroom 5. So could you explain more clearly what you have done?
You need to BUY Lightroom 5 Upgrade (about 80 dollars) and then type both the Lightroom 4 and 5 License Numbers in the program. You can update to DOT versions of Lr4 for free but Lr5 is an UPGRADE and costs. Lr6 is rumored to be out soon so you may want to wait a month as you can upgrade from 4 to 6 and skip 5.
If you purchased a Lightroom 5 upgrade license key you need to first enter this key when prompted, if you are installing on the same computer where the prior version i.e. LR 4 is installed the license key will also be recognized automatically. If not you will be prompted to enter the previous key to complete the install.
There is no need to uninstall LR 4 prior to installing the upgrade to LR 5.
All makes sense now: I was using the License Number from Lightroom 4, without realising I also needed the Lightroom 5 License Number. Thought Upgrade was free! Naïve, yes. I'll wait on and buy Lightroom 6 upgrade.
Thanks to all who replied,