Of course not,the frame of iPhone 5S is different from iPhone 5C.And the Home button hole is different too.
Before replacing your broken screen,please check carefully what your iPhone model is.
Here is the picture of the [http://www.ecever.com/blog/difference-iphone-5s-iphone-5c-lcd-screen-digitizer-assembly/|difference between iPhone 5S and iPhone 5C LCD Screen]:
[image|311455|align=left]