Final answer:
The primary purpose of Gaspar Pérez de Villagrá's writing is likely to describe the difficulties faced during the expedition, in the context of seeking recognition from the Spanish crown similar to probanzas de méritos written by other conquerors such as Columbus. Option number C is correct.
Step-by-step explanation:
The main purpose of Gaspar Pérez de Villagrá's writing in the given excerpt is most likely to describe the difficulties faced during the expedition.
As a participant in Spanish expeditions, Villagrá's narratives were often part of the larger experiences of conquest and colonization, akin to the probanzas de méritos or reports written by Spaniards to justify their endeavors to the crown, explain the challenges they faced, and often to seek rewards or recognition for their efforts. His accounts, along with those of others like Christopher Columbus, Hernán Cortés, and Francisco Pizarro, served not only to document the exploration but also to exemplify the European perspective on the newly encountered lands and peoples, filled with personal bias and sometimes fantastical elements.