If you have the choice, leave on Christmas day; the roads will be much quieter.People are already at their destination.You will have a good run south on I-5 and if you leave that early - will be there in plenty of time.I find chewing a toothbrush a great help in warding off drowsiness and make several stops to stretch and take a break.
On Christmas Day, I-5 itself is less crowded than the day before. However, when you hit LA, the traffic is very dense. Actually, these days it starts around Magic Mountain.If you leave at 7:00 AM, you ll have plenty of time, although I would recommend leaving even earlier. Be prepared for some major sun in your eyes as you approach I-5. In a perfect world it takes about 5 hours, so stopping to rest/gas up and traffic would add another hour or so. And if you get drowsy, definitely do not drive it at night. There s nothing to break the monotony.
LA has really bad traffic... maybe you can fly instead on the morning of Christmas, driving on or flying christmas eve is not a good idea.