[tex]\begin{gathered} \text{ Since 11 is odd, 11\textasciicircum{}7 is odd} \\ \text{ Since 7 is odd, 7\textasciicircum{}5 is allso odd, And since we know that odd+odd=even, } \\ 11^7+7^5\text{ is an even number} \end{gathered}[/tex]
Thus, the smallest prime factor of 11^7 +7^5 is 2
