Advantages of Adobe Photoshop Lightroom version 3.4 over version 5.0

Lightroom 5 and Lightroom 3.4 are different apps. LR5 was obsoleted about 5 years, being replaced by LR6. LR6 in turn was replaced by LR7, but was renamed at that point to Lightroom Classic. Lightroom Classic is currently at version 9.4. At the same time as Classic was introduced, a similar but separate app was introduced, confusingly given the original Lightroom name, and which is now at version 3.4, so that is what you appear to be using. Both Classic and Lightroom are subscription-only, and are available together in one of the Adobe Photography subscription plans, though there is also a Lightroom-only plan. The major difference between Classic and the new Lightroom is that like LR5, Classic manages images from the local hard-drive(s) whereas Lightroom stores the images in the Adobe cloud. Being a newer program, Lightroom does not yet have all the functions of Lightroom Classic, but the edit tools are broadly similar (as both use the Camera Raw engine for image development).

Here's a blog post setting out the differences between the two current offerings, which may help you decide which, if any, subscription you might want: https://www.lightroomqueen.com/lightroom-cc-vs-classic-features/