I download the Combo Updater in preference to activating Software Update as the combo will iron out any problems from previous versions. An old habit which is still valid.
Sometimes, the combo page takes a little while to get updated after a release is issued and I just wait. And I run updates when I have window of low activity., just in case.
You can get the OSX 10.9.5 combo updater from the Apple Support page here.
Afterward, run Software Update for Safari to be upgraded from version 7.0.6 to 7.1.