Help with example RSA problem
You don't appear to have done anything wrong; you can double check your result by computing:


  $16657^5 \bmod 16781$


and find that it is indeed 5347; that is, 16657 is the number that, when encoded with the public key, results in the value you were given.

I suspect that moral of this story is that random examples on the internet might be worth just as much as you pay for them.