Hey Tweety.

The easiest way to do this is to use powers of 2. Look at 5 mod 11, then 5^2, then 5^4, 5^8, then 5^10 and finally 5^11.

As an example 5 mod 9 = 5. 5^2 mod 9 = 25 mod 9 = -2. 5^4 = (-2)^2 mod 9 = 4. 5^8 mod 9 = 16 mod 9 = -2. 5^11 mod 9 = -2*-2*5 mod 9 = 20 mod 9 = 2.

Check to see if I have made a mistake, but the process used above is the basic idea in solving these kinds of problems.