On a similar note, what do you do when a creature is pushed into a wall with forced movement. In 4e they used to take damage I seem to remember. I assume 5e has no rules covering that too ?
Nope. I house rule a d6 for every 10 feet further they would have gone.
I like it.
Myself, I'll often have hitting the wall knock them prone.
I don't do that (yet) but I could see a saving throw based on amount of damage taken. I'd probably make it a con save, but that's just because there are already too many important dex saves.