Yes, the PLC inputs have hysteresis. The input voltage needs to rise above 10.5V in order to turn OFF the input.
If you only have a 5V digital output, you could use a simple transistor to drive the PLC's digital input. You could also use a very low cost IC such as ULN2003A to interface to the PLC's input.
Another way is to connect your 5V digital output to the PLC's analog input and periodically monitor the analog readings of this input and if it is above certain reading, turn on a relay and when it is below certain reading, turn off a relay. The relay then can be used in the ladder diagram like a digital input for your program.