Output waveform for this circuit
No, as the voltage across the capacitor increases the voltage across the resistor will fall from 5V to 0V. At that point current stops flowing and the voltages remain constant...forever.

EDIT: For the capacitor to discharge you need a resistive path from one terminal of the capacitor to the other (without the 5V source in series). There's just no path to discharge the capacitor. I don't know how to explain it more simply.