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Can plugging public earphones in our iPhone 5's audio jack pose any security risk? Can our data (pictures, videos) be accessed? How often one can try a unknown earphone into iPhone 5c's audio jack in term of security and privacy risk?
There is no security risk. That is only audio and no data access is possible.
But there maybe some health concerns if using previously used earphone that are not sterilized. Whipping them with a germs killer wet-tissue or alcohol should do it.