iphone 5s dead battery and need to get photos out of it.

The phone has to be able to turn on.

Were you using iCloud Photos? If you were, your photos should be there too, as well as on other devices such as a computer..

If you cannot do that, you will ahve to get the phone to a state where it can be recharged. Try taking it to an Apple Genius Bar and ask about your options. Particularly ask them if replacing the battery really means replacing the battery in that phone, not an entire exchange which is typical for other repairs. Of course if they do an entire exchange you get an empty phone. Urge upon them the importance of getting your phone back intact. Your other option along these lines is to go to a third party repair service since they actually repair phones and you don't really care about the phone after this. Of course Apple won't ever look at it again if you take it to a third party place but you don't really care about that from what you said.