iPhone 5s boot looping

My phone is now stuck in a restart loop. Shows the apple, goes to grey screen, black screen, return. I’ve tried the hard restart (home button and power button held down at once), but that just restarts the restart loop. Now what? :(

Aaaaaaand now the screen is broken again AND I’m stuck in the boot loop. (Broke screen trying to put it back together again. When I pressed glass into place, snapped the end that wasn’t broken on my old screen.) Still boot looping. What a bummer. Help with the bootloop anyone? Not ordering another screen ‘til I know how to get the thing started again. :(