Reducing powers modulos

Question

Was working on a problem and reached this last part where I got an answer of $93^5 \bmod 95$. Anyone knows how to reduce $93^5 \bmod 95$ without using a calculator?

Thanks!

Answer 1

Well $93\equiv -2\bmod 95$ so we have $$93^5\equiv (-2)^5\equiv (-1)^5\cdot 2^5\equiv -32\equiv 63\bmod 95$$