I have a Microsoft Sculpt Comfort Mouse that has a middle button with horizontal scroll, but it doesn't work in Plasma 5. It DOES work in Plasma 4. Is there any way e.g. through synaptics, for getting this feature and making it stick?

CORRECTION: It does not work in Qt5 apps! I just tried it out in Firefox and it works flawlessly (I've been using Qupzilla as my browser).

Doesn't work with my touchpad either! Is horizontal scrolling broken in Plasma 5?

What testcase?

Works for me in eg. kate, but that WinXP-clone icon view in dolphin reacts on vertical scrolls, while it's horizontally layouted.

I tried Qupzilla, Kate, Dolphin--all Qt5 builds. I'm running Plasma 5.4.1 and Qt version 5.4.2. Must be a packaging thing with Kubuntu. I'll file a bug.

Could be a problem with (usage of) libinput (in in return whether the device generates touch events, button 6/7 events or both)

So it's now working in qupzilla on my laptop's touchpad, but not using my mouse on my desktop (same distro). I'll dig a bit and see if I can test to see whether the mouse buttons are registering horizontal scroll events.

You can use "xev" to check for differences in the event generation.
"xev -event button" will produce less spam, but might stash differences.

The button events are being registered, and it works in GTK apps like Firefox, it just doesn't do anything in my qt5 apps like kate and qupzilla.

I think that I have an issue that might be related.
My mouse buttons are remapped using xinput to switch left wheel tilt with the middle button.
This way instead of pressing the wheel I use left tilt as the middle button click.
It's just easier and I use it a lot.
It has been working great for years, and it still does with everything based on GTK or KDE4.
Xev also reports correct button numbers.

It was working fine in Plasma 5.3.2, but since I upgraded to Plasma 5.4.2 it doesn't.
Plasma 5 apps register left tilt as horizontal scroll left.
No matter what. It ignores remapping with xinput.
Also switching buttons 6 and 7, which should result in reversed horizontal scrolling is ignored.
For Plasma 5, left tilt is left horizontal scroll, and right tilt is right horizontal scroll.
And I haven't found a way to change it...

This will not relate to the Plasma release version, but either some Qt5 update - or you're now using libinput instead of evdev.