Supercapacitor backup circuit - why seperate charge and discharge path?
For your circuit as drawn, anything connected to the 5V supply would be powered by the cap.  This would include any regulators that may be supplying the 5V.  If the 5V only ever comes from a cable the situation is better, but you'd still have that 5V on some (presumably) exposed terminals.

To add to your pain, the resistor would just waste energy as the cap was discharging.

However -- for some simple battery powered thing where you just want to keep the micro going when the batteries are being replaced (or similar purpose), what you have there may actually work.