However, if you strictly need the 2013 versions for a legacy project (e.g., opening an old iPhoto library), you need the Apple-supported "Migration" path.
If a friend or family member bought iLife ’13 when it was free or paid, you can sign into the Mac App Store on your older Mac (running Mojave or earlier) with their credentials and download from Purchased. Then switch back to your ID.
Open the Mac App Store, search for "iMovie" and "GarageBand," and click "Get." It takes 30 seconds and won't brick your computer.
iLife '13, released as a 2013 update for OS X Mavericks, was distributed as individual, free apps via the Mac App Store rather than a bundled .dmg file. Users seeking this software should utilize the Purchased tab in the App Store, as third-party "full dmg" downloads carry security risks. For more details, visit Apple Support Community Apple Support Community What's Wrong With Setup.exe? - Coding Horror
Originally, iLife was a comprehensive suite including tools like iWeb and iDVD. By the 2013 release, the suite was streamlined to focus on three core applications, which were eventually distributed individually through the Mac App Store: iMovie (v10.0):
: Downloading a “DMG” from an unofficial source for an old suite like iLife ’13 (which doesn’t officially exist as a single DMG) exposes your Mac to potential exploits, especially since those apps are no longer updated.