Staple food tends to have inelastic demand, so a 5% drop added onto a shortage for stochastic reasons could have significant impacts on prices, with resulting social disruptions. Like Michael Tobis, I'm not sure why some people find this climate/food price issue to be such a strained argument.
I should note that the study gave an overall figure and not a specific for extreme conditions. Maybe climate change moderates the extreme conditions - or maybe not, and it makes extreme conditions worse so that the 4-5% figure is an underestimate in bad times. I'd guess the latter is more likely than the former, but we'll have to find out some other time.
The same study says North American hasn't been hit, yet. We'll have our turn at some point though.