Laura, I'm going to move this to ArcGIS Desktop Installation support which is a better location. GeoNet Help is actually just for help in using the forums.
edit: I stand corrected. I don't have permission to move it to that location. But tagging it about will still allow it to get more looks re: installation.
...in the meantime, you may want to look at some of the suggestions https://community.esri.com/message/736775-re-arcgis-10-clean-uninstallation?commentID=736775#comment...
If you want to follow along, why not keep 10.5, then when you go to save your project to use on another machine... use the Save as Copy option and select the lower version.
Only stuff that is 10.5 that wasn't in 10.3 will get stripped out, but for most classes that shouldn't be and issue