This is a question relating the fundamental behavior of git. You want to merge the changes from a branch to another branch while treating deletions as "no change". But basically, I think, that is impossible, because git treats deletions as changes and hence reflects the deletions on merge.
In your specific case, master still contains file3.txt, file4.txt, file5.txt and these 3 files are not modified in any sense on branch master.
But in the branch 'edit_branch' they have been removed (preferably by git rm) and hence changed on edit_branch.
So, now if you merge 'edit_branch' to master, git will see that master is basically an ancestor commit of edit_branch, and hence will do a fast-forward merge by simply designating the latest commit of edit_branch as master. That means it will always reflect the deletions.
But if the files on master are modified after creation of the edit_branch, then git will at least show merge CONFLICTS on the deleted files, thus telling you about which files have been deleted and hence need being taken care about.
So, basically there is no direct way of doing what you want to do. But a probable workaround would be to do some dummy modifications (like adding a single whitespace in the end / or writing a comment explaining why the modification was done) on all files on master, just after creating edit_branch. Then even if you switch to edit_branch and delete some files there accidentally, at least you'll get notified about it during merging and get a chance to handle it before merging.
I would like to add that such deletion-merge scenarios are never really useful in any known real use cases. When you delete some files on a branch just to keep the directory clean and make the branch intentionally different from the core, you do not merge it to the core thereafter. For example, in case of github-pages, we create a branch gh-pages and delete every file other than the webpages on that branch, effectively hiding unnecessary content from the branch. But we do not find the need to merge gh-pages back to master.
PS. If you are coming home during the convocation, consider buying me a beer :)