Classic LR desktop updates [How to open Sony A6400 Raw files with LR 5.6?]

And if you open this bit of Adobe 101, you will see that you need Lightroom Classic v8.211  or newer, so no upgrade to v5.whatever or 6.whatever will help. 

https://helpx.adobe.com/camera-raw/kb/camera-raw-plug-supported-cameras.html

note that the Lightroom v2.2.1 listed is not the old pre subscription Lightroom

To edit your Sony RAW files in your current Lightroom will require an DNG converter, you can then edit the DNG files

That is right. As far as Lightroom Classic is concerned, the "cloud" is primarily a delivery system utilized to keep Lightroom Classic up to date. However, Lightroom Classic is installed on your computer hard drive, utilizes a local catalog, and stores images on your local hard drive(s). You only share images in the cloud if/when you choose to do so. Lightroom Classic is much improved over Lightroom 5, in my opinion, and well worth the subscription if you are in to your photography at all.

"Hi, how do I update my classic LR 5.6 without going to the cloud version?"

Do you realize that the current version of Lightroom Classic is not a "cloud version"? It runs entirely on your computer, the photos are located entirely on your computer, and you don't ever have to share your photos in 'the cloud'. (Now it is true that the software downloads to your computer from "the cloud", and once every X days, Lightroom has to validate you have paid your subscription by checking with the Adobe validation engine in "the cloud", but otherwise, this is not a 'cloud version' of software)

Adobe presently offer no perpetual license key Lightroom applications, the last version was Lightroom 6 and the last update was V 6.14 released in Dec 2017.

Purchase of this version continued for many months and ceased before the end of 2018. The License key requires online registration to activate. Even if you located CD version in a used bin somewhere it would be v6.0 and it would be virtually impossible to activate.

Lightroom 5.6 is not Lightroom Classic. It is an old outdated version of Lightroom that isn't updated anymore. The last update that was ever issued for Lightroom 5 was 5.7.1, but I doubt that you will ever be able to find a download for it. If you don't want to go to Lightroom Classic then you have a couple of options. You can download the free DNG converter and convert the raw files to DNG files that are compatible with Lightroom 5.6. Your other alternative would be to consider Photoshop Elements. It utilizes the latest version of Camera Raw, and therefore would support the raw files from your Sony camera. There is no provision to update Lightroom 5.6 to accommodate the native raw files from that camera model. As far as Lightroom itself is concerned, that camera model wasn't supported until Lightroom Classic (the subscription version) 8.2.1.