First you have to set the direction of the pin (DDRC)
Then write a 1 or 0 to the pin. You change the values of the register as a whole, so you have to use bitwise operators.
DDRC |= (1<<PORTC5); //Set pin 5 (the 6th) as an output - the data direction register wil be 'OR'ed with 00100000'
PORTC |= (1<<PORTC5); //Turn pin on port register will be 'OR'd with the same value above.
PORTC &= ~(1<<PORTC5); //turn pin off - port register will be 'AND'ed with the inverted form of 00100000, which is 11011111.
That should work. DDRC only needs to be set once.