wash them with vinegar!
1. mix 1 part of vinegar (white or apple cider probably work best) and 10 parts of water.
2. dump the berries into the mixture and swirl around.
3. drain, rinse if you want (though the mixture is so diluted you can't taste the vinegar,) and
4. pop in the fridge.
The vinegar kills any mold spores and other bacteria that might be on the surface of the fruit, and voila!
Raspberries will last 1 week or more, and strawberries go almost 2 weeks without getting moldy and soft.