The capo just raises the tone by the number of frets you position it at. And each fret raises the tone by one semitone.

Hence - if you play a C chord without capo, then the same shape chord with capo at fret 1 makes it a C#, at 2nd fret it is D and so on.

Similarly, because all the notes are raised by a semitone per fret then it follows that the same applies to the key. So a song in C when played open is in D if capo at 2nd fret, is in E if capo at 4th fret, and is in F if capo at 5th fret.