Lost almost 35 GB, Grand Perspective shows that as "Misc Files"

Still think it might be Time Machine. Is it a laptop (and you sometimes disconnect from the backup drive)? Go through this:

About Time Machine local snapshots - Apple Support

CleanMyMac is dangerous - it sometimes deletes essential files - I'd uninstall it. And don't bother with other "fix-your-Mac" products!

Never use apps like CleanMyMac or MacKeeper and the like. They are capable of doing so much harm that you have to format the disk and install everything anew.

Does GrandPerspective give the address where these 35GB are: post that address here.

There's also a very large (5+ GB) file in lost + found but I heard those should be ignored...

You should boot from the recovery partition, and run Disk Utility -> Verify (or even Repair). Then again it was most likely Disk Utility Repair that put the file in lost+found.

A file in lost+found is a file that was found during Disk Utility Repair that did not have a directory entry pointing to it. Normally this should not happen (even abnormally it should not happen; that is why metadata journaling is used by HFS+). Anyway, the file was found and since the name only exists in directory, and there is no directory entry, the file is given a numeric name based on its internal inode number.

Anyway, chances are you an delete it. You will need admin privilege to delete it.

And then follow the link greg sahli has given you about Time Machine snapshots that are collected when your Mac cannot access the Time Capsule.

About Time Machine local snapshots - Apple Support

If that does not work for you, then see this article on running OmniDiskSweeper as 'root' so you can find "Everything" on your storage.

OmniDiskSweeper (free download)

<http://www.omnigroup.com/more>

When using OmniDiskSweeper, or any utility that shows all your files... See the following article if you want to run it as root

<http://www.macobserver.com/tmo/article/how_to_recover_missing_hard_drive_space>

Chances are the tricks suggested by MacObserver can be used to invoke GrandPerspective as a root user as well, if you prefer GrandPerspective.

Try OmniDiskSweeper instead of GrandPerspective.

As long as you do not know what those files they are, you should not attempt to delete them.

If they are TimeMachine so-called "local snapshots" (as greg sahli thinks), they do not hurt, and they will be used and deleted when you connect the TimeMachine backup disk. They also disappear when space gets scarce. There is a Terminal command to not do these local snapshots. You have to set that again however after each OSX update.

On a SSD it is better to disable these local snapshots, as Garbage Collection has to do extra work after these snapshots are deleted.

The Terminal command is (copy/paste):

sudo tmutil disablelocal

Lex

That can well be local snapshots. These files disappear automatically after switching off local snapshots.

Great, have fun.

Lex