Super Capacitor Charge and Discharge Circuit
What you have will work, although D12 is pointless.  The problem is that when the cap is discharging onto the 5 V line, there will be a drop across D13.  Using a Schottky as you show is a good idea, but the drop will still be around 1/4 volt.  Another problem is that the voltage will go lower over time with the amount of charge drained from the cap.

You might consider putting the energy backup capacity before the power supply.  That might allow the stored energy to be used more efficiently, and the voltage will stay regulated for a while.