Peak Power Vs Rated Power
You are running class D, so to hit 250W BTL you will want somewhere in the region of about 65-80V or so assuming a single rail design and an 8 ohm load, dual rail would be +-35V to +-40V or so. 

Now the 50W number tells you how to size heatsinks, but 5 seconds is forever in semiconductor junction terms so there is not a lot to be saved in the sand, it still needs to handle worst case voltage and current.

There is a bit of a trap, with a reactive load you can wind up with the amp supplying power to the supply during part of the cycle, make sure nothing exciting happens under these conditions. 

On the subject of current, again reactive loads rear their heads, you can wind up with peak current demands very much greater then steady state on real program material, I would design the supply to run at least twice your calculated peak power for 100ms without tripping for overcurrent.