Sorry to hear that you're getting an invalid serial error, please try the solution mentioned & let us know if it helps:
Delete the activation database files
Activation database files that are corrupted or have incorrect file permissions can prevent your product from installing correctly.
- Delete the Adobe PCD folder and caps.db file from the following locations:Windows:
- \Program Files\Common Files\Adobe\Adobe PCD
- \Program Files\Common Files\Adobe\caps\caps.db
- /Library/Application Support/Adobe/Adobe PCD
- /Library/Application Support/Adobe/caps/caps.db
- Restart your Adobe application. Enter the serial number when prompted.If you are not prompted to enter a serial number or the application won't open, uninstall and reinstall the application.
- Uninstall the application, if necessary. For Creative Suite applications, uninstall the entire Creative Suite, not just a single application.Note:If you are having problems with a stand-alone version of Lightroom, you must uninstall several files manually, after running the uninstaller. For instructions, see Uninstall Lightroom manually.
- Reinstall the applications, using the Creative Suite installer and serial number.Note:You can download the product directly from the Other downloads page on adobe.com, and then reinstall.
- Start your application.
Thank you Sahil, another collegue from you helped me in the meantime. LR5 is already running on my MAC