Five and half hours are more than enough for any half way reasonable operating condition. However, in January its possible that you will encounter outlier conditions such as a major snow storm. There is no guarantee against that, and no safety margin will be truly "safe", even if you fly in the day before. While it's not likely to be that bad, it can happen.
If you are really worried about this scenario, your best bet is to book everything on a single ticket, even if it's a little more expensive. The main advantage would be that the airline could route you through a different hub from Seattle if Chicago turns into a mess. If you were to fly with United, they could route you through Newark, Washington, San Francisco, Detroit etc. Even if you get stuck in Chicago, the airline would eventually get you through to your destination at no additional cost.
If you miss your flight in Chicago, you can plead with the connecting airline, but chances are they will charge you at least a change fee. Another thing to consider: if your flight from Chicago is delayed or moved to the next day, you'd have to rebook or change your first flight from Seattle to Chicago too.