Try to clean the charge hole on this S5 and then try to charge it.
1) Try to connect the phone with USB cable to computer. If it starts to charge... you need to change your adapter.
2) Try to connect your phone to another charger and see what happens.
remember that if your phone is at 0% (its not real 0% but the phone shows that) the phone will need 5 or more minutes to charge a bit and starts up again.