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.

Ignore this question. I was searching for the wrong brand… I'm sleepy

Not by your chinny-chin-chin. Nikon uses the F-mount while Canon has the EF-mount. They are not compatible.

For your T5i, you can use lenses that have the EF or EF-S mount. Don't buy EF-M. Most modern Canon lenses (aside from EF-M) will fit. Just beware of the FD, FL and other older non-AF lenses that are not compatible to the EF mount.

If you really must dabble with cheap lenses, get an M42 to EF/EOS adapter and hunt for sub-$50 lenses with the M42 screwmount. There are lots available at eBay and fleamarkets. Make sure the glass is clean and the aperture blades work properly. There will be no autofocus but you should get focus confirmation. You will also be limited to shooting in manual mode and depending on the camera model, Av mode.