- May 3 Spanish silver fleet sails to Panama
- May 7 Admiral Hermites conquering fleet reaches Callao the Lima, Peru
- May 8 Hungarian King Bethlen Gabor & Holy Roman Emperor Ferdinand II sign Treaty of Vienna
- May 10 Dutch admirals Jacob Willekens and Piet Heyn conquer Salvador da Bahia (Brazil)
- May 13 Admiral Hermites' fleet blockades Lima, Peru