installing Safari back on Yosemite 10.10.5

Safari is part of the OS and cannot be deleted, so what did you do. If you just removed the icon from the dock at the bottom of your screen you can put it back by opening your Applications folder and dragging the icon back into the dock. As Safari is part of the OS there is no individual download for Safari, try downloading this, Download OS X Yosemite 10.10.5 Combo Update

once downloaded open your Downloads folder and double-click on the .dmg file to start the installation.

If the above doesn't work, do a backup, preferable 2 separate ones on 2 drives. Boot to the Recovery Volume (command - R on a restart or hold down the option/alt key during a restart and select Recovery Volume). Run Disk Utility Verify/Repair Disk and Repair Permissions until you get no errors. Then re-install the OS.

Reinstall from macOS Recovery

OS X Recovery

OS X Recovery (2)