iPhone 5s won't turn on just shows Apple logo
iphone had already been laging all day but my battery died i plugged it into charger and it is now stuck on Apple logo
Force your device to start. To do this, press Sleep/Wake and Home buttons and hold them for at least 10 seconds.
If this does not help, take a look these Apple Support articles:
If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support
Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.
As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. You will need to have iTunes installed on this computer. Keep the Home button pressed until you see the iTunes logo on the screen of your iPhone. After that on your computer you should see the iTunes window saying your iPhone needs to be restored to factory settings. Click on the restore button.
More info here: https://support.apple.com/en-us/HT201263