What is the exact error message?
Are you attempting to install the same version as the one that was one the old PC?
Which version of LR and what is your OS?
All may be pertinent.
Then you more than likely downloaded the Creative Cloud version of LR and not the Stand Alone version. By chance did ytou install the Creative Cloud Desktop app and then from that install LR.
It is tough to find the download page for the stand alone version. Adobe keeps sending you to the CC version which won't accept a stand alone serial number. Here is a link for you.
If you need it for Mac just Google Adobe Lightroom 5 for Mac download.
Here's a link to that.
Yep, that's exactly what it was. It's all working tickety boo now. Thanks heaps to you and Nic Hamilton for your help. Cheers.