Why are some old images downloaded from the web always sorted under "Today" in Gallery? When I open the gallery and sort by Time, there is always a section "Today", and it has several images I downloaded from the web...... months ago.

That's literally it. Why are old images showing under "Today"? There are other images I got from the web that are actually correctly sorted in older sections. But under "Today" I got around 20 web images that have been sitting there for months.

One thing I noticed is that this doesn't happen with photos taken with the phone. Such photos are always correctly sorted. So it's something with web images.

Android 5.0, Galaxy S5.
You may want to look into some EXIF editors to edit the metadata of those images (specifically the time). I can't name any great editors in particular, but there are plenty of apps and programs available as I looked through. If I find any good ones, I'll be sure to tell you the names of them. Best of luck!