I currenlty have LR 5.5 and want to upgrade to the newest version. I can't seem to find the link to do this on Adobe's website. I am an Adobe Create Cloud subscriber.
In the CC desktop app on the Apps tab select Previous versions. LR 5 should be listed there with an Update button to the right. Click that Update button.
If you are a CC subscriber you can get the newest LR 6.4 which would install into its own directory/folder and then copy your LR 5 catalog file and convert that copy to a LR 6 catalog file. That is if you are running a 64bit computer with a 64bit operating system. LR 6 only runs on 64bit computers and operating systems.