Can you replace an iPhone 5s to newer models?

I recently dropped my phone at work, and now the screen is very glitchy, at times I can use it but it gets frustrating when it acts up, I’d have to put the brightness on low setting cause if it’s any higher then my current setting the screen won’t work. I’m well passed the AppleCare coverage so I was wondering if I could just back up my 5s phone and get a new phone like a 6 or 6s maybe?

Thanks