LAWRENCE: please read this reply and not the one above: I hadn't finished writing and it wouldn't allow me to continue...this is the final, and good copy:
Thanks Lawrence.
By "safe", I mean, if I delete the AAE does that delete the associated .jpg? By the sounds of it, it does not; it only deletes any formatting I've done (I don't tend to edit my photos or videos; I'm an amateur:). I use iPhoto; is this a Photo "App"? If not, I don't think I use a Photo App. I take photos on my iPhone 6 and import them to my external hard drive. That's about all I do. The AAE files that I have all seem to be in my Trash; for every file # there seem to be 2 AAE files associated with it:
Trash:

They also seem to be videos: (under "Kind" it says Slow motion Video Sidecar). *Are* these videos, or photos? Would this suggest I edited the videos? I don't think I did, at least, I've not done so to my knowledge.
If these are in the trash, can I delete them, and assume the "viewable" format (not .jpg but whatever the video extension is for videos)-is in my iPhoto library? Or does the above suggest to you that both formats have been deleted? I only see AAE files in the Trash.
Also-just a quick observation: the file names in my Trash (the # that corresponds to each file: 5195, 5196 etc.) don't necessarily correspond to the files/videos I see in the iPhoto album where my photos are located; the images *are* however in Finder, sitting under iPhoto library. So, if I go into Finder, and look for the corresponding AAE file # (but as .jpg-not AAE) I can see the same # (5195) as the ones in my Trash. But if I open up the iPhoto App and look in my album for 5195; 5195 isn't there.
Another observation: in iPhoto, the missing file #'s that aren't in my album, *are* in "Photos" under the heading "Library" in the iPhoto App.
So, am I understanding correctly, that if I delete a photo from an album, the corresponding file # will disappear, with the photo, but that the photo remains "live" (it exists) in Photos under "Library"? In other words, the files that are in my Trash, *can* be seen as .jpg's in Photos under "Library" in the iPhoto App, but they are no longer in the album (I think I deleted them from the album as I had many duplicates). Am I correct in thinking that the Photos under "Library" in the iPhoto App correspond to the .jpg's that I see in Finder, that sit directly under iPhoto Library?
This is what I see on my External hard drive....

and:

I'd like to see if the 5195 *is* the same file as the AAE in the Trash, but obviously can't view the AAE version. Is there any way to view the AAE files to check which .jpg's they correspond to, or am I to trust that the # is accurate and corresponds to the .jpg with the same number? Am I to assume the AEE 5195 file in my Trash *is* the same file as the one in the Photos, under "Library"?
Many thanks.....