Before I added a second fridge, I used dry ice for week long trips on the water. I have a 165qt Igloo cooler
that I'd pack with three 9 lb blocks of dry ice and 3 frozen 1 gallon water bottles. I'd wrap each flat square of dry ice in newspaper and tape it up with package tape. I placed a thin wood plank on the cooler bottom to prevent cooler cracking from the extreme cold and made up dividers for the cooler to allow for 3 compartments. Each compartment got a block of dry ice and a pre-frozen fresh water ice jug.
Pre-frozen foods were added in order of planned use so the first-used would be at the top. I kept the cooler on the cool fwd stateroom settee and covered it with beach towels for added insulation. As the food level dropped, I stuffed the towels into the space at the top to provide better insulation.
The frozen steaks and water bottles were still frozen on day 5 when the dry ice was almost gone. The water bottles were still partially frozen on day 7 and the food stayed very cold, but not frozen on day 7. As a side benefit, the water was then cold and drinkable.
If you plan to leave your cooler unopened for the 5 days, I suspect you'd get better dry ice endurance. If your lazarette is warmer than my fwd stateroom (75 degrees max), you might lose some effectiveness.
Jeffnick and Cpeudonym have posted of their experiences with a frozen brine solution in place of fresh water and dry ice. I believe a blend of the two, dry ice and frozen brine, would yield excellent results, but I have not tried it yet.