To verify the DMG's checksum on a Mac, open and run the command shasum -a 256 /path/to/your/file.dmg , making sure to replace the file path with the actual location of your downloaded file.
The OS X Yosemite 10.10.5 update includes the new Photos app and improves the stability, compatibility, and security of your Mac. Apple Support OS X Yosemite Part 1: Upgrade Step by Step