I need to downgrade to OS Mavericks 10.9.5 from a new pre-installed Yosemite 10.10.1 iMac late 2013, can you help me out? Is it possible considering Yosemite was pre-installed?!
The first pre-installed OS on the iMac14,1/iMac14,2 was Mac OS X 10.8.4. You may install any OS version newer than that one.
If you have any personal data on this Mac, save it to an external drive.
After creating a bootable thumb drive using the Mavericks installer, boot to the thumb drive, erase the main disk and install Mavericks.
Restore your personal data from the external drive. Some of the data (Photos library, probably your Mail data) - if you had any - is not backward compatible with the apps (iPhoto, Mail) used in Mavericks.
The short answer is – yes, you can.
The not-so-short answer is, it's messy. You can't downgrade, according to all the problems I had with personally trying to. But then I found a working method which I carried out on my own Mac. Sure, it worked, but my Mac is different from yours. It should work, but there's not 'warranty'. As long as you have all your files backed up to an external hard drive, you should be good.
If you want, you can just try to downgrade using a Mavericks installation package.
Nonetheless, here's my working method. Prepare...
First, find an image of OS X Mavericks that you want to downgrade to. Right click on it and select Show Package Contents >> Contents >> SharedSupport and extract InstallESD.dmg to the Desktop. Now convert it to a bootable image (it's hard, but feasible). Transfer the bootable to an external hard drive.
Then you've gotta back up your Mac using TimeMachine.
Then go into Recovery Mode by restarting your Mac and holding down the Command and R keys before the boot sound.
Now open Disk Utility (from the top menu), select the very top disk on the left (above Macintosh HD), open the Partition tab, and add a partition by clicking the + (plus) icon below. Call it whatever you want, adjust its size to about halfway (for now) and click Apply.
Now insert your external hard drive. In the top menu choose Images >> Convert and find & click on the Mavericks image from the inserted drive. Click Convert and then Cancel (yes, you read that correctly).
Now your image appears in the left bar of Disk Utility. Click on it and now drag the partition which you created earlier (should be below Macintosh HD) to the Destination field. Click Restore (and then Erase if it asks you for confirmation).
Once it is finally over, go back to the very top hard disk and to the Partition tab. Remove the old Macintosh HD partition by selecting it, deleting it using the - (minus/dash) icon, and resizing the newly created Mavericks partition to the maximum size remaining. Apply the necessary changes and wait again.
Now finally reboot. Congratulations, you have successfully downgraded from Yosemite to Mavericks without any hassle (might have understated the difficulty a little).
If the instructions I listed are impractical, then sorry for wasting your time. But be warned in advance, that 'playing around' with disk partitions is a joke of no kind. One f*** up and you might lose the Recovery partition. And that is one thing that no Mac user wants to do.