The conclusion of 1 Peter (1 Peter 5)

The ending of 1 Peter perhaps provides a surprise with which we can re-interpret the whole book.  It comes off a surprise ending to a mystery story and we can see something else was happening all along.

Peter says in verse 13:  "She who is Babylon, chosen together with you, sends you her greetings, and so does my son Mark.".

It is a little cryptic, but I think Peter means he is in Babylon, I.e., Rome.  If he is in Rome and referring to it as "Babylon", then he is likely a prisoner.

Another clue could be found in 2 Timothy 4:11 where Paul specifically requests that Mark come to Rome.

As for Silas, he travelled extensively with Paul.  See Acts 16-18.  His formal named, Sylvanus, is also mentioned in Paul's Epistles to Corinth and Thessalonica.  (2 Corinthians 1:19, 1 Thess. 1:1, and 2 Thess. 1:1).  
Non-canonical tradition and sources indicate that Peter was martyred in Rome, perhaps at the coliseum.  The story goes that he did not want to be crucified like Jesus, so the Romans crucified him upside down.

But why is Peter in Rome?  We know Paul went to Rome because he was arrested and Paul, being a Roman citizen, appealed to Caesar.  Peter was not a Roman citizen and would not have had the luxury.  If he went, he probably went voluntarily.  But the Gospel was shifting to the Gentiles and Rome was the greatest Gentile city at the time, being the capital of the Empire.

Looking back at the rest of 1 Peter, if Peter is writing from Rome, then Peter knows first hand suffering for the church.  But yet, he does not mention it and certainly does not complain about it. Rather, he spends the letter encouraging others who are suffering.

It also gives some interesting insight on his advice on obeying one's political rulers (2:13-17), passive resistance (2:23-25), and specifically, "honor the king".  (2:17).  Peter could very well be on the way to his own martyrdom at the hands of the Roman soldiers yet encourages others to obey the very same government that is about to kill Peter.