[tex]2^{123}=2^{4\cdot 30+3}=(2^4)^{30}\cdot2^3=16^{30}\cdot8=\overline{...6}\cdot8=\overline{....8}\\
3^{123}=3^{4\cdot 30+3}=(3^4)^{30}\cdot3^3=81^{30}\cdot27=\overline{...1}\cdot27=\overline{....7}\\
2^{123}+3^{123}=\overline{....8}+\overline{....7}=\overline{....5}=>\\
(2^{123}+3^{123})\vdots5[/tex]
