For a very graphic example of the type of economic disruption that climate change can and likely will bring for many places, look to Pakistan—which has already been feeling the brunt of weather weirding in the form of massive flooding in recent years.
Pakistan's Daily Times reports that the former Federal State Minister for Environment Malik Amin Aslam has said that the nation is looking at $14 billion dollars per year in losses (that's the 5% of GDP part) due to both climate-related disasters and other losses.
The Minister noted that Pakistan is one of the lowest emitting nations in the world, yet is in the top 10 nations to be worst-affected by climate change. He also said that both the frequency and intensity of climate-related disasters is going up, as in the damages in monetary terms. In the past three years, the nation's top three disasters have occurred, with 60% of "maximum natural disasters" happening in the past 10 years.
An important economic note regarding GDP: Remember that GDP measures all economic activity in the nation. So, in the case of a massive disaster, the cost of rebuilding afterwards increases GDP—meaning that if an economic indicator that took into account a broader spectrum of economic activity (such as the Genuine Progress Indicator), the real damages to Pakistan are likely larger than that 5% GDP loss indicates.