After a long time I have to care about a LS installation and do updates.

currently installed version is Version 3.17.3+190429

Now I'm looking for a version compare regarding requirements and features of that version to latest versions. 
is it correct, that there is no further 3.x-support?

Especially I have not found what were the big changes with 5.0,5.1,5.2
What is the correct workflow for an update from 3.17 to 5.2? what work has to be done?
 

Step 1: update to latest 3.x version
Step 2: review the use of themes: if you just use the default themes (Vanilla, Fruity or Bootswatch: there is not a big problem, just update an review you surveys. They may need minor adjustments in the theme options.
If you use custom themes you will probably have to adjust the themes. Contact the developers that have developed these custom themes.
Step 3: update on a separate server and see if everything works. If so: update on live server. If not: make adjustments or hire someone to do that for you.