Software // System/library/frameworks -> deleted QTKIT.framework Deleted by accident -> QTKIT.framework folder. Finder crashes on start-up as do most applications. 

Any idea how I can restore this? No time-machine back up.

Yosemite 10.10.5
macbook pro 2011
Boot to Recovery HD and select reinstall OS X.

That will reinstall the current OS and repopulate the frameworks that are missing. This isn't designed to erase your Mac, but you are flying without a safety harness with no backup.