Staying five more days is significant, so I would pick January. Just be aware that there will be cold days - in fact, your entire trip could be cold. My DH and I visited in mid-December. We had one really hot day, followed by the rest of our trip being in the low 60s as the high and high 30s in the lows. Yes, lows in the 30s. Watch the weather and pack accordingly - my DH did not bring a coat, him being a real "macho" guy (hahahaha) and stating that a sweatshirt would be just fine! Well, by the end of the trip, he had a fever. Sigh. With that said, it was nice to have the option to dress warmer rather than the alternative of us going at a very hot and humid time with no relief from the weather. In December, we were comfortable most days - it was just night time when it got rough. We enjoyed going in the hot tub at our resort with the cold weather, and we would get hot cocoa in our resort refillable mugs at the pool bar for the walk back to our room. It wasn't all that unpleasant, considering. You can get a lot more done at the parks with the weather feeling cool and comfortable rather than being miserable and heat-sick.
If you do not plan to return to WDW, I highly recommend taking time for rest and relaxation. My DH and I have visited Disney together four times now - this trip in August will be our fifth. In the earlier trips, it was all about "getting everything done." While that was really fun, doing the parks every single day was exhausting. I have flat feet; walking for more than 13 miles every day takes a huge toll. My DH and I both regularly had shin splints by the time we returned to our hotel. I enjoyed my trips most when we didn't park hop like crazy. My ideal trip would involve doing a park every other day. On the off days, sleep in, visit Disney Springs, go mini-golfing (some packages receive free mini-golf), enjoy the hot tub, check out the Boardwalk (at NIGHT - not during the day), etc. One thing that we love to do is watch the Magic Kingdom fireworks outside of Magic Kingdom. We once went to the Polynesian, shared a Dole Whip, and watched the fireworks on loungers on the beach - it was sooo relaxing and magical. They even turn down the lights and play the fireworks soundtrack all around the resort. Our FAVORITE, though, is treating ourselves to a fancy meal at Narcoossee's at the Grand Floridian. We get a reservation right before the fireworks and can watch from our table or the dock just outside the restaurant. They also turn down the lights and play the fireworks soundtrack. We usually opt for a full steamed lobster (we don't get fresh lobster too often in Wisconsin) and a steak and share the meals. For you, coming from Washington, maybe you wouldn't be as wowed with the lobster, but who knows?
One last thing: I know from research that some attractions are closed for refurbishment in January. You may want to research this and see if there is anything scheduled that would be a deal breaker. If not, I would definitely pick January over October - lower crowds and more comfortable weather would always win for me!