They are related to Nintendo. You see, the PS5's predecessors are the PS4, PS3, PS2 and PS1. Before Sony made the PS1, they created a CD-based addon for the SNES. The SNES is made by Nintendo.
The Xbox was developed when their Windows 9x/NT had games and developed a game console during the Dreamcast/GBC era. They named it the "Xbox" and released it after Sony released the PS2 and at the same time during the GameCube and tried to buy Nintendo. Both are related to Nintendo but THERE'S NO SUCH THING AS A NINTENDO! (Nintendo is not a noun)