Their website does not seem to offer the option of downloading a "standalone" version anymore and I don't know what is feasible but, assuming you owned the copy of LR5 that was working on your old PC and had the install disks, you should be able to put it on the new machine. What is frustrating is that you cannot "deactivate" the old version to activate the same product on a new machine, however. Same thing happened to me when my old PC decided to give up the ghost and my restore from backup would not install LR. Spend some quality time with Adobe support. It is a bit of a hassle, but they can helped me activate it on my new machine through their workaround.
Now if you do not have the install disks, do a "search" on adobe.com. It takes a bit of looking, but you can find an LR 5.4 download that they say will install on a machine without any previous additions of Lightroom installed. Then, it is all about activation (see above).
The standalone version is still available, it's just bloody hard to find on their website. They are really trying to push people into CC, which is complete BS in my opinion.