iPhone 5s acting quirky. Turned off to reboot, now Apple symbol comes up for a minute or so and then shuts off. Won't turn on

iPhone 5s has been acting weird for a few days. Apps shut down without notice, etc. Got message storage almost full, deleted some apps, photos, messages, and then turned off to reboot. When I try to turn back on, the Apple logo comes on for about a minute, then the screen goes black and the phone is dead. Had about a 60 percent charge when I turned it off.