Is a Nikon AF-S dx nikkor compatible with a T5i?

It's a 55-200 mm lens. I just got a T5i body and I wanted to buy some cheaper beginner lenses first but I don't know what is compatible and what is not.

Read more: https://nikonmag.com/talk/lens/is-a-nikon-af-s-dx-nikkor-compatible-with-a-t5i.html