Can I use the Canon EF-S 55-250mm f/4-5.6 IS STM lens on my Nikon D5200 body?
No, you can't. In general, lenses made for one brand can't fit on another brand without an adapter, and in this case, there are no good options.
Using a "naive" mechanical adapter would end you up with a macro lens that you would have to focus by moving the whole camera (or using a helicoid/bellows equipped adapter set) and that you could not set the aperture on. While such a use case exists for some lenses (in hardcore macro/studio photography), a zoom lens is an exquisitely unsuitable choice for it.
Modern Canon lenses are among the hardest to adapt to other brands of camera body (due to there being no or insufficient mechanically operable controls nor mechanical linkages). Nikon bodies are among the hardest to adapt non-native lenses to (due to very high flange distance). Also, this lens appears to be "fly by wire", the rings on the lens really are NOT mechanically linked to zoom and focus.
Also, adapting AF lenses will in most cases only yield very dissatisfying functionality, unless specialized and expensive "smart" adapters are involved (which do exist for using Canon EF lenses on some DSLMs, but not so much for using them on DSLRs). This seems to be especially true of lenses (including Canon EF/EF-S and KM/Sony A mount. Compare Nikon and Pentax fit lenses.) that are designed to only fit a line of cameras that is AF equipped across the board.