Why won't my iPhone 5s hold a charge?

I know it's not my cable or the port that s screwed up, I plug my charger in and it shows the white screen with the apple logo. But that s all it does, it goes from black screen to white screen perpetually, until I take the charger out in which case it won't turn on at all. What could be wrong with my iPhone?

It's old.

Apple 5s, that's like back from the Jurassic isn't it?

The battery in it probably failed.

I think Mark is right.
You may also want to see what it does if you plug it into your computer.

The Walnut Creek California Apple Store told me $50 to replace a iPhone 5 battery. I think Best Buy may have been a little more.