Statement I: Since the only way to avoid a prime total while ensuring three coins from the set would require the inclusion of certain combinations, and excluding the coin of denomination 5 leads to totals that are prime; thus, if m is not prime, 5 must be included.

Statement II: The sum of digits can yield multiple total combinations (such as 3, 6, 9, etc.), and these do not definitively force X to have received a coin of denomination 5, allowing for totals that can avoid it entirely.