Using Capacitor to provide a short blast of high voltage

If I charged a 1F Capacitor to 5V is there a way I could get a brief blast of say 1kV or something like that

Yes, connect it to a huge transformer.

You don't need the huge capacitor. Just get a 12V power supply and an ignition coil. You will get many many kilovolts out of it if you use a MOSFET to switch the primary windings on and off. Just do a google search for ignition coil driver.

Capacitors store energy in a way that the voltage is whatever voltage they were charged to. You can get a huge current as the capacitor is discharged, but the voltage is never higher than what the capacitor was initially charged to.

Inductors (transformers) store energy in a way that the current through them while they are being "charged" will continue to flow after they are disconnected, which creates a huge voltage.

Speakerguy hit it on the head best I think. A capacitor discharged through an ingnition coil is going to provide quiet a burst, but it depends a lot on the series resistance of the primary coil and the super cap itself.

Any iron core transformer will saturate when connected to a fully charged 5V 1F capacitor, unless is huge.

I think an air core transformer is best.

Beware, the energy is 12.5J which will is quite likely to be fatal if discharged into the human body in a 100ms or so.