May Revolution
The May Revolution was a direct reaction to Spain's Peninsular War. In 1808, King Ferdinand VII of Spain abdicated in favor of Napoleon, who granted the throne to his brother, Joseph Bonaparte. A Supreme Central Junta led resistance to Joseph's government and the French occupation of Spain, but eventually suffered a series of reversals that resulted in the Spanish loss of the northern half of the country. On February 1, 1810, French troops took Seville and gained control of most of Andalusia. The Supreme Junta retreated to Cadiz and dissolved itself, and the Council of Regency of Spain and the Indies replaced it. News of these events arrived in Buenos Aires on May 18, brought by British ships.
Sun of May
The specification ""of May"" is a reference to the May Revolution which took place in the week from 18 to 25 May 1810, which marked the beginning of the independence from the Spanish Empire for the countries that were then part of the Viceroyalty of the Río de la Plata. A legend claims that as the new government was proclaimed, the sun broke through the clouds, which was seen as a good omen.