if your car is only loosing 1 quart over 5,000 miles it may not necessarily indicate that the engine is burning the oil. There are several factors that dictate the ammount of oil an engine consumes, the 2 biggest are the volitility (tendency to evaporate when heated) and your driving habbits.
There's other things as well, such as the oil may not start to get consumed until it gets to, say, 3,000 miles, after that some of the oil's physical properties start to degrade due to thermal breakdown and contamination from combustion by-products. As the oil degrades it becomes more volitile or more likely to evaporate. So, in most cases the engine isn't burning the oil, the oil is just evaproating.
So to combat this try either changing the oil more often, or switch brands.