Find $r$ for $3^{574} + 26^{1347}\equiv r\mod 5$ Even though I'm looking to solve the problem, could anyone also point me out any sort of "strategy" to solve similar exercises? 
I know the things I must make use of most are the congruence properties and Fermat's little theorem, but I have a hard time applying them and finding out how to solve a problem.
Any help is greatly appreciated.

Start with $3^2 \equiv -1 \mod 5$ and $26 \equiv 1 \mod 5$.
