The computer once read the iPhone 5s but now it has forgotten that I upgraded to a 5s. Explain.
What do you mean that your computer "reads your iPhone 5s as ... iPhone 4"? Where are you seeing that it "read" the iPhone model incorrectly?
Did you restore your iPhone 5S from an iPhone 4 backup? Is it doing something strange with the phone or is the issue just a "name" thing?
On your iPhone, go to Settings > General > About and look at the first field on the screen ("Name"). Is it correct? Is it incorrect? Is it the source of the issue? You can change it by tapping on the name and editing it.
Otherwise, can you explain why you think it's a problem so we can understand and try to help.