Same here, just bought a standalone licence and it's rejecting my serial number. Is it any wonder why people pirate Adobe's software when it's legitimate systems are so broken.
The protection system is so elaborate because people try to pirate the software incessantly and sometimes the elaborateness leads to fragility or misunderstanding about what to do.
There are several different kinds of LR (educational, enterprise, standalone, cloud, etc) and if the serial number is being rejected and was bought at a legitimate reseller, rather than someone selling pirated or stolen serial numbers, then it is possible it is being typed into the wrong kind of LR or even the wrong version (4 vs 5).
If you are using an educational version there may be a separate download you need to use—I’m not sure because I’ve never purchased an educational version of LR, but if there is a distinct version to download then there should be some instructions, somewhere (packaging, e-mail), that tell you that different location.
For a non-educational, non-enterprise, single-person standalone license, the version of LR 5 to download is the LR 5.6 link near the top left of this page: http://www.adobe.com/downloads/updates.html
If you have installed a different kind of LR, such as the CC version, then you may want to uninstall it before installing what you download from the link, above.
. Is it any wonder why people pirate Adobe's software when it's legitimate systems are so broken.
People pirate Adobe software because it's very good software, and because the world is full of cheap, dishonest scumbags who would rather steal than pay for what they want.
Since you asked...
Nope, bought the standalone LR5 from the Adobe website after the trial expired (not installed via CC, standalone version) and they managed to screw it up and I'm not even given a freephone number for their customer services, instead I have to phone London FFS.
Fact is, I can't even uninstall. It was not installed via CC, and the instructions to remove the standalone version are wrong, you cannot drag the application to the trash can (Manually uninstall Lightroom) and there is no uninstaller for LR under Applications->Utilities in OSX.
I don't condone piracy, what I'm referring to is that is it any wonder people pirate it when they put barriers in the way of legitimate sales. This isn't the first time I or other people I know have run into difficulty with Adobe's broken services.