Can I use my Nikon D5100 batteries on my Nikon D5600?

Could there be any damage?

Both use the En-El 14 battery.

A simple, easy search on the specs of each camera will tell you they use the same battery.

Yes, you can use a D5100 battery on a D5600 camera. But the D5100 battery has a slightly less capacity than the D5600 battery. Furthermore, D5600 camera uses up energy a bit more because it has a larger LCD screen and more intensive processing. So in sum, you can use the D5100 battery on a D5600camera, but the battery duration will be only slightly shorter, but not much.

AFAIK, the only difference is mAh so I guess it's okay.

The battery chambers are a keyed fit. So if the battery fits, you can use it.

According to Nikon, the D5100 uses the EN-EL14 while the D5600 uses (or comes with) a EN-EL14a. The "a" version has more power and will work in both.

Be certain to only use Nikon brand batteries. Nikon is so greedy that they put electronics and software in their DSLRs to detect whether you're using a Nikon branded battery or not. If not, then the camera is designed to shut off. Way to go Nikon!

Check and see if it is the same type of battery, if it is, then no problem!

I have to disagree, I'm afraid. I had a large # of 'non-nikon' batteries that worked wonders in my D5100. Suddenly, none appear to work on my new D5600, I get a display on the screen saying the battery is not useable. This is idiotic, even the high-power Bower battery isn't recognized as useable.

Oops. See the issue was already addressed. Yes, big thanks… Nikon. Next camera may be a Cannon. Once I recover from having to buy $250 or worth of 'new' Nikon batteries.