a) should be relatively simple (use the Markov property of the S_n) and for b), think about it in this way, suppose you are at 0 and want to go to 1. You have to roll either a 1, or a 5 (both give remainder 1). So from 0 to 1 has probability 1/3. Now try to figure the other ones out using the same method.
Hope this helps.