In fact it all depends on the versions of solidworks that are installed on your PC, you can use settings saved with the latest version and use them with the 2015 version.
Wouldn't you have installed SolidWorks twice in a row in different locations ?
DSL, I answered a little too quickly yesterday, I think it doesn't offer you the previous versions because your settings must be saved under the 2016 version.
So for 2016, it was the first time I installed it.
On the other hand, my settings file is from 2015 and edited to replace 2015 with 2016 (I have directories of template files by version...). I have to test it next time.
The SW settings before 2016 changed when I opened the 2016 software, I was surprised when I went from 2014 to 2016 (and yet I had checked all the options that I wanted to start from scratch and then import the preferences).
Anyway it saved me 20seconds but hey :-)
In absolute terms, I think you must have problems with common registers and records, etc. to have so many versions installed on the computer.
Not really a complete and absolute answer but I think that the fact that I edit my settings file (to replace "manually" 2015 with 2016) makes SW panic a bit (there must still be references to SW15 that I haven't seen).
A piece of advice already said, but it's good to remember it:
when we do a major update (year version) of SW,
It is preferable to take screenshots of its settings (system options, DWG-DXF export options, etc...)
Then if you delete the existing SW, restart the pc, then manually delete the remaining folders (programs, progdata, users/AppData...) as well as take a look in the register in the right places!
Then restart
Then install the new version
...
Why do this? because it allows you to start with a healthy bass, not to drag "mysterious bugs", not to have new interesting options disabled by default, etc...
Of course, it takes a little more time, but the benefit can sometimes be great (disappearance of some bugs).