How can I maximize the storage life of fresh beef in the refrigerator?
If you can get a good tight wrap of plastic wrap around it and store in the bottom of your fridge, where the temp should be approaching 32F it should last out the 5 days just fine. If you have a rub in mind for it you might apply that first then wrap and store. 

Remember that beef is usually hung anywhere from 5 to 30 days at 33F in quarters before being butchered. If you don't have a thermometer for your fridge, get one (or two even, one high and one low) so you have a good idea of what your temp range is. If the coldest region of your fridge is over 35F you should turn it down some. See @HoboDave's answer for a better commentary on fridge temps.