When you installed the Lightroom 5 on your MacBook, did it ask for both serial numbers. Since you purchased Lightroom 5 as an upgrade, you need both the serial number from your original purchase as well as the new serial number for Lightroom 5. If you have both of those numbers and they are still not being accepted then you will have to contact Adobe customer support for a solution.
Yes it asked both serial numbers on my old mac, but now I using the new macbook, just downloaded from the internet and trying to use the serial numbers but no success.
All I can say is that it is "supposed" to work. But I have seen a few comments recently that others have experienced your same problem. I haven't followed those discussions close enough to know what the solution is.