What are examples of natural disasters that took place in the last 5 years?
Hurricanes, floods, tornadoes, earthquakes, and snowstorms (blizzards) are just some of the natural disasters that took place in the past 5 years.
I'll attempt to compile a non-exhaustive list of some specific instances of natural disasters.
Hurricanes and floods:
North American Storm Complex- October 2015; hurricane induced flooding in North Carolina, South Carolina, Florida, New York, New Brunswick (Canada); 25 fatalities total, 12 billion USD in damage (in South Carolina alone)
Hurricane Sandy- October 22- November 2, 2012; hurricane induced flooding and storm surge: entire Eastern Seaboard, Haiti, Cuba, Dominican Republic, The Bahamas, Jamaica, Canada, and Puerto Rico; 233 fatalities, 75 billion USD in damage
2011 Joplin Tornado- May 22, 2011; isolated tornadic event nearly leveling the entire town of Joplin, Missouri; 162 fatalities, 1,150 injured, 2.95 billion USD in damage
(Tidbit of trivia: the Joplin Tornado is the most costly tornado in the past 30 years)
2011 Super Outbreak- April 25- 28, 2011; numerous tornadoes in within a 3 day span across Alabama, Mississippi, Arkansas, Georgia, Tennessee, and Virginia; 348 fatalities, 2,200 injured, 11 billion USD in damage
(Tidbit of trivia: during the outbreak hail was recorded in Virginia with a diameter of 11 cm)
2011 Tōhoku Earthquake and Tsunami- March 11, 2011 an initial earthquake magnitude 9.0 (on the moment magnitude scale) and 11,450 aftershocks (since 2015) plus a tsunami of 40.5 meters, the while the entire Pacific Rim was affected by the tsunami, Japan ( Tōhoku region) suffered the worst from both (earthquake and tsunami); 15,894 fatalities, 6,152 injured, 2,562 missing/ presumed dead, total economic cost of 235 billion USD
(Tidbit of trivia: the Tōhoku Earthquake is considered the costliest economic disaster ever recorded)
2015 Nepal Earthquake - April 25, 2015 over 8,000 people died on this day and the 7.8 earthquake caused an avalanche on Everest, killing 24 people (the most in history). A 7.3 aftershock from this earthquake in May, 2015 killed over 200 people.
January 2016 United States Blizzard- January 22- 24, 2016; immense amounts of snow in the Northeastern United States, atypical snowfall as far Southeast as New Orleans, Louisiana (spanning across the entire Gulf Coast); 55 fatalities, total economic cost of 3 billion USD