Hi, as I said I called someone from apple and my Iphone 5s works fine now, I had a blue screen and it always tried to start but after a while there came a blue screen, if you have the same issue as I had you can try the next thing, it worked for me, what u acctualy reinstall the software on your phone.
Be sure the phone is turned off.
Open itunes and take a cable to connect your phone to you mac/pc
Hold the home botton and connect the phone with your mac. keep pressing the home botton.
now on you Iphone you will see a itunes logo, and there will open a window on your mac.
then you simply have to follow these steps and you will reinstall your software again.
at the end you can if you can put everything back on your phone with itunes or icoud, at least as you took a backup from your phone.
if you have the same problem again after these steps, than I might go to an apple store.
I hope I can help someone with this.
greetings
Lukas