Yes it is that crowded. There is a chance MK will be closed to new guests by mid morning on some days (almost always on 12/25 and 1/1). But it usually reopens later in the pm. None the less, lines are long and crowds are heavy all days.
However, Disney can still be fun during this time. Park hours are longer and there are lots of extra activities. Since you are both 23 you can handle long days and some running around.
Here are some tips:
1) If you are staying on site take advantage of early entry. This is a must, especially for MK.
2) Make an itinerary and/or touring plan. Know what rides/attractions you want to do first and what you are willing to skip. Do the busiest rides first, before the crowds build (especially useful with EE). This sometimes involves walking from one end of the park to another just to get on a ride (ie: go from SM to Splash without stopping for other rides).
3) Get a guide book. They are full of info. I like the Unofficial Guide since they provide great touring plans. If you follow the touring plans you will see many attractions/rides. Other popular guides are Passporter and Birnbaum's.
4) Make Priority Seatings for any restaurants you want to eat at. If you don't you could wait hours for lunch or dinner at a sit down restaurant--especially at Epcot (which has some great restaurants).
5) Use Fast Pass!! Use Fast Pass!! Use Fast Pass!! In all seriousness, this will really help you. Make sure you understand how to maximize it's effectiveness (get second FP as soon as possible and before using first FP, have one person run and get the next FP while the other person waits in line at another ride, get the FP even if the standby line wait is less than the return time for FP--go on another ride or eat a meal while waiting for the return time).
Itinerary Suggestions:
1) See Fantasmic at MGM, Illuminations at Epcot and Fireworks at MK
2) See Cirque du Soleil at DTD. It's a little expensive but worth the money.
3) Eat at some nice restaurants. Epcot is loaded with them and it's a great chance to try something you don't get at home. The deluxe and moderate resorts also have good sit down restaurants and are worth checking out as well. Make PS for them.
4) Check out the Christmas decorations at the resorts.
5) Check out the Adventurer's Club at PI. Make sure you see a "show" in one of the rooms--they are hilarious. The Comedy Warehouse is fun also.
With five days you can do a lot. However, you must understand you will not be able to do everything. That's okay. Enjoy what you get to do. Everything else just gives you an excuse to return in a few years.
Good luck and have fun