Your question is twofold - how (or if) you can downgrade from 16.04 to 15.10/14.02, and how to upgrade correctly to 15.10.
Downgrading is possible, but a tedious and risky process, with no guarantee of restoring your system as it was. See this question for more details.
If you want to upgrade (after the downgrading) to 15.10, it can't be done directly, according to the answers here. You have to upgrade to every release in between, to 14.10, 15.04, and finally 15.10.
I recommend simply removing your new 16.04, and installing 15.10. Recently, I asked how to upgrade from 15.10 to 16.04, and I was advised to do a clean install. That is only one release apart.
So even though a clean install is quite a process, it seems to me it's less of a hassle than downgrading and upgrading in baby steps. Just remember to back up all of your user files, before you start.