Why are my applications crashing after the update to 10.10.5?

Just guessing:

My standard install of OS X Yosemite 10.10.5 doesn't contain the file /System/Library/Frameworks/AppKit.framework/Versions/C/AppKit..

Please check the following:

1. the currentness of your backup
2. The proper destination of the soft link "Current" in the folder /System/Library/Frameworks/AppKit.framework/Versions/. It should be /System/Library/Frameworks/AppKit.framework/Versions/C/.
3. Does the folder /System/Library/Frameworks/AppKit.framework/Versions/C/ contain a second file named Appkit.?

4. If the folder /System/Library/Frameworks/AppKit.framework/Versions/C/ contains a second file named Appkit., check the md5s (md5 /path/to/file) of the files Appkit and Appkit.. The md5 of the file Appkit in my system is 5404e155c41dedd1bea5e29bf02182d8 (size=39.450.864 bytes, mod date 2nd of June 2015). If you have 2 files Appkit and Appkit. with identical and correct md5s move Appkit. to a save place with:

   sudo mv "/System/Library/Frameworks/AppKit.framework/Versions/C/Appkit." "/System/Library/Frameworks/Appkit."
   

   If one has the correct md5 and the other a wrong md5, remove the file with wrong md5 and if necessary rename the correct one to "Appkit". If both md5s are wrong reinstall 10.10.5 with the 10.10.5 Combo Updater. Reboot your Mac and test the behavior of µTorrent. If the testing with µTorrent gave a positive result remove the file /System/Library/Frameworks/Appkit.

5. If the folder doesn't contain a file named "Appkit." at all boot to your Recovery HD and try repair your main volume.