It is really REALLY simple, if you have a complete TimeMachine backup.
The Yosemite is somewhere in October last year upgraded to ElCapitan as far as I remember.
Not everything is downwads compatible as already stated, but that is no problem with a TM backup.
When you are sure that your TM backup contains everything from before the ElCap backup (you can check that now, by TM->Enter TimeMachine->scroll back in time until the beginning of October 2015).
1. Connect the TM disk, if it is not already connected.
2. Shutdown the Machine.
3. Start Up while holding the CMD+R keys, it is s l o w, when you see the progress bar is started, you can let go of holding the 2 keys;
4. When fully started there appears a window with a menu, start the "restore from TimeMachine"
5. Indicate the TM disk, then point to the Startup Disk: It will first erase/format the Startup disk (that is why you must be sure that the TM disk has that period inside !!).
6. Select the last backup on the TM disk, that has 10.10.5 on it (it is indicated in the time list), then go on
7. All in all it will take some time, prepare...
8. When ready it will startup in Yosemite.
9. You will have to add all files that have a later date: Mail should be synced again when IMAP, or imported (not copied) into Mail when Pop, the same for some other apps (iPhoto, LTR,...), just files can be added by copying with Finder.
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If you have no TM disk, it is a more difficult process...