Pausing sawtooth generator given an input
I need a way to keep the output at 5v given a while a certain input
  signal is high


Use an analogue switch to connect 5 volts to the 0.01 uF capacitor. Use an analogue switch that can run from 15 volts and make sure it has a lowish on resistance so that the 5 volts is not affected by the current source.

Alternatively, use a MOSFET and a resistor across the 0.01 uF capacitor. The MOSFET should be N channel and have the source grounded. The resistor value should be 100 kohm so that 50uA*R = 5 volts.