Do you have an earlier version of LR prior to LR5?
You normally need both serial numbers to activate.
If you originally had Lightroom 5 installed on your older notebook with that same Upgrade License serial number then you at some time had an older version of LR you used as the upgrade path, a serial number from that older version. You will need to find that older version serial number and input it to activate LR 5 on your new computer.
If you originally registered your product the serial number will be stored in your Adobe account. Click the red logo (top left on this web page) sign-in, and then click the Manage Account button. It should be possible to browse your purchase history. You are looking for a 24 digit number commencing 1160.