Spoiler! Sneak Peek of Castle Season 5, Episode 10, “Significant Others”: Rick and Kate Question an Unhinged Murder Suspect (VIDEO) Tweet January 2, 2013 at 04:21PM EST by Alyse Whitney Related: Castle, Spoilers , Sneak Peeks , Caskett , Richard Castle , Kate Beckett , Season 5 Episode 10 Credit: YouTube While Rick and Kate question a murder suspect, things take a turn for the creepy. Is this unhinged man a danger to our favorite couple? We’ll have to wait until Monday to find out!Original Air Date: Castle Season 5, Episode 10: “Significant Others” airs on Monday, Jan. 7, 2013 at 10 p.m. ET on ABC.