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Ellen White is considered a prophet and can gain insights like this through inspiration.
Some Adventist would consider her writings only a few steps short of the inspiration of the bible.
Further, the detail of age is relatively insignificant. The bible clearly states that Samuel was a child and under the guidance of Eli when God first spoke to him.
Weather he was 5 or 12 probably doesn't matter in the grand scheme of things. He wouldn't have been 13 or older as this is a transition to manhood in Jewish culture.