The error in the sentence "I have not met him since five months" is the incorrect use of the word "since." In English grammar, "since" is used to indicate a specific starting point in time from which an action or state has continued (e.g., "since Monday," "since 2005," "since he left").
However, when referring to a duration or a period of time, the preposition "for" should be used. "For" specifies the length of time an action has occurred (e.g., "for five months," "for two hours," "for a decade"). In this sentence, "five months" clearly denotes a duration, not a starting point.
Therefore, "since" must be replaced with "for" to make the sentence grammatically correct. The accurate sentence is: "I have not met him for five months." This distinction between "since" and "for" is vital for expressing temporal relationships accurately, especially when using perfect tenses in English.