Can i replace my iPhone 5 housing with an iPhone 5C?

I've dropped my phone a lot and the screen hasn't cracked at all, although the metal frame and back are decorated in heavy dings, deep scratches and chipped paint. I'm looking on eBay and i'm finding new housings although i also see iphone 5c ones. I want to know if i can just take my iPhone's screen and put it in an iPhone 5c housing.

I don't think its possible

No.
iPhone 5 and 5c are completely different.
Size and shape are totally different.
Just Google some pictures