My new iPhone 5s keeps randomly crashing and showing the Apple-icon!

connect the iphone to the computer make sure you have the most recent version of itunes and back up the iphone then click on restore which is under the summary tab if that does not work then call apple support

I had the same problem but also had the deadly blue screen. Had to go to an Apple store to have it fixed. Mine was some type of overload with a file and icloud. Apple had sent me a new replacement had the same thing happen. I couldn't get anything would just revert to the apple screen. All fixed!!! Had to restore as a new phone.