What are possible consequences for the screen, when doing the replacement of iPhone 5s home button
As long as you apply common sense when replacing Touch ID/the home button you should be fine:


all screws go back to the same thread they came from
tighten the screws so they won't stick out
make sure to properly align the screen to the top of the case first
pay attention to the flex cables - put them in all the way into the ZIF connector


I recommend to watch a few 5s display repair videos if you never have replaced a screen before. This should give you a better idea what diffuculties may arise.