I draw a star with the

Is it possible to change the color each corner of the star individually?

Imagine we create a star with 5 corners. How we can make it colorize by 5 different colors?

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There probably are a few different ways to do it. Here's what I would do.

1 - draw the star
2 - Path menu > Object to Path
3 - engage snapping to nodes and snap to center of objects
4 - use the Pen tool and draw diamond-ish paths for however many points in the star in the following manner: click once over one of the existing nodes to start the new path; click consecutive nodes including the center of the object, when you get to that area; and finally click once at the same place you started, to end the path
5 - you could either color the original star one of the colors, and make 4 new paths (for a 5 point star) for the other colors; or make 5 diamond-ish paths and later delete the original star

Of course it's possible, based on your question, that you don't want points in the center. Maybe you only want the color in the spikes, while the center area would be a 6th color. But you can probably modify my instructions to do that? Of course, you wouldn't need to snap to the center of the object, in that case