Very dificult one as high current Zener diodes are expensive and can be unprodictable at high speeds.
I would try a IN5343B and see if it stands up if not you will have to move up to BZY 93 but I could only find them at 8.2v The diference in price is over £12.
You could allso try exstending the current range of your zener by using a transistor (2n3055) heatsinked. This is still considered resonable practice.
mystery i don't think using only a diode is a good idea, 5 A is very much and even using a single transistor might not be safe depending on the voltage you want to stabilize. please provide some more info
The 1N5333B series from ON Semiconductor https://www.onsemi.com/pub/Collateral/1N5333B-D.PDF should meet your needs. It will take 180 W for 6 ms which means it will also take 60 W for 25 ms which meets your need.
The usual way to incrase the power rating is to put the zener between the collector and base of a BJT. The TIP35 series is frequently used. The collector and emitter leads are then used as a zener whose voltage is about 0.8 V higher than the real zener. This works as sort of a current divider. Only 1/beta of the total current goes through the physical zener diode. The rest goes through the BJT collector. It all comes out the emitter.