[tex]5\equiv5\mod{16}[/tex]
[tex]5^2=25\equiv9\mod{16}[/tex]
[tex]5^3\equiv5\cdot9\equiv45\equiv48-3\equiv-3\equiv13\mod{16}[/tex]
[tex]5^4\equiv9^2\equiv81\equiv1\mod{16}[/tex]
[tex]5^5\equiv5\cdot1\equiv5\mod{16}[/tex]
[tex]7\equiv7\mod{16}[/tex]
[tex]7^2\equiv49\equiv48+1\equiv1\mod{16}[/tex]
[tex]7^3\equiv7\cdot1\equiv7\mod{16}[/tex]
